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<h2>SL Paper 3</h2><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define<em> proper length.</em></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96<em>c</em> relative to the Earth. Calculate the pion’s lifetime as measured by an observer on the Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth reference frame, the pion moves a distance Y before the pion decays. Demonstrate, with calculations, how length contraction applies to this situation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An electron X is moving parallel to a current-carrying wire. The positive ions and the wire are fixed in the reference frame of the laboratory. The drift speed of the free electrons in the wire is the same as the speed of the external electron X.</p>
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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define <em>frame of reference.</em></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the reference frame of the laboratory the force on X is magnetic.</p>
<p>(i) State the nature of the force acting on X in this reference frame where X is at rest.</p>
<p>(ii) Explain how this force arises.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Identical twins, A and B, are initially on Earth. Twin A remains on Earth while twin B leaves the Earth at a speed of 0.6<em>c</em> for a return journey to a point three light years from Earth.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time taken for the journey in the reference frame of twin B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, for the reference frame of twin A, a spacetime diagram that represents the worldlines for both twins.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest how the twin paradox arises and how it is resolved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer P sitting in a train moving at a speed <em>v</em> measures that his journey takes a time Δ<em>t</em><sub>P</sub>. An observer Q at rest with respect to the ground measures that the journey takes a time Δ<em>t</em><sub>Q</sub>.</p>
</div>
<div class="specification">
<p>According to Q there is an instant at which the train is completely within the tunnel.</p>
<p>At that instant two lights at the front and the back of the train are turned on simultaneously according to Q.</p>
<p style="text-align: center;"><img 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"></p>
<p>The spacetime diagram according to observer Q shows event B (back light turns on) and event F (front light turns on).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_14.55.20.png" alt="M17/4/PHYSI/SP3/ENG/TZ1/4d_02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State which of the two time intervals is a proper time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed <em>v</em> of the train for the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta {t_{\text{P}}}}}{{\Delta {t_{\text{Q}}}}} = 0.30">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mtext>Q</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.30</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Later the train is travelling at a speed of 0.60c. Observer P measures the length of the train to be 125 m. The train enters a tunnel of length 100 m according to observer Q.</p>
<p>Show that the length of the train according to observer Q is 100 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ct'">
<mi>c</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
</math></span> and space <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x'">
<msup>
<mi>x</mi>
<mo>′</mo>
</msup>
</math></span> axes for observer P’s reference frame on the spacetime diagram.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, using the spacetime diagram, which light was turned on first according to observer P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Apply a Lorentz transformation to show that the time difference between events B and F according to observer P is 2.5 × 10<sup>–7</sup> s.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Demonstrate that the spacetime interval between events B and F is invariant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second train is moving at a velocity of –0.70c with respect to the ground.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Calculate the speed of the second train relative to observer P.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> prediction of Maxwell’s theory of electromagnetism that is consistent with special relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A current is established in a long straight wire that is at rest in a laboratory.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A proton is at rest relative to the laboratory and the wire.</p>
<p>Observer X is at rest in the laboratory. Observer Y moves to the right with constant speed relative to the laboratory. Compare and contrast how observer X and observer Y account for any non-gravitational forces on the proton.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket of proper length 450 m is approaching a space station whose proper length is 9.0 km. The speed of the rocket relative to the space station is 0.80<em>c</em>.</p>
<p style="text-align: center;"><img 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"></p>
<p>X is an observer at rest in the space station.</p>
<p> </p>
</div>
<div class="specification">
<p>Two lamps at opposite ends of the space station turn on at the same time according to X. Using a Lorentz transformation, determine, according to an observer at rest in the rocket,</p>
</div>
<div class="specification">
<p>The rocket carries a different lamp. Event 1 is the flash of the rocket’s lamp occurring at the origin of <strong>both</strong> reference frames. Event 2 is the flash of the rocket’s lamp at time<em> ct'</em> = 1.0 m according to the rocket. The coordinates for event 2 for observers in the space station are <em>x</em> and <em>ct</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-27_om_07.57.21.png" alt="M17/4/PHYSI/SP3/ENG/TZ2/05c"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of the rocket according to X.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A space shuttle is released from the rocket. The shuttle moves with speed 0.20<em>c</em> <strong>to the right</strong> according to X. Calculate the <strong>velocity</strong> of the shuttle relative to the rocket.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the time interval between the lamps turning on.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>which lamp turns on first.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram label the coordinates <em>x</em> and <em>ct</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the <em>ct</em> coordinate in (c)(i) is less than, equal to <strong>or </strong>greater than 1.0 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <em>c</em> <sup>2</sup><em>t </em><sup>2</sup> – <em>x </em><sup>2</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="question">
<p>Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above ground and move downwards at a speed of 0.98<em>c</em> relative to the ground. For this speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span> = 5.0. Discuss, with suitable calculations, how this experiment provides evidence for time dilation.</p>
</div>
<br><hr><br><div class="specification">
<p>A spaceship S leaves the Earth with a speed <em>v </em>= 0.80<em>c</em>. The spacetime diagram for the Earth is shown. A clock on the Earth and a clock on the spaceship are synchronized at the origin of the spacetime diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle between the worldline of S and the worldline of the Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the diagram, the <em>x′</em>-axis for the reference frame of S.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An event Z is shown on the diagram. Label the co-ordinates of this event in the reference frame of S.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A long current-carrying wire is at rest in the reference frame S of the laboratory. A positively charged particle P outside the wire moves with velocity <em>v</em> relative to S. The electrons making up the current in the wire move with the same velocity<em> v</em> relative to S.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a reference frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the force experienced by P is magnetic, electric or both, in reference frame S.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the force experienced by P is magnetic, electric or both, in the rest frame of P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two parallel current-carrying wires have equal currents in the same direction. There is an attractive force between the wires.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations describe.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a postulate that is the same for both special relativity and Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the nature of the attractive force recorded by an observer stationary with respect to the wires.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second observer moves at the drift velocity of the electron current in the wires. Discuss how this observer accounts for the force between the wires.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A spaceship is travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>80</mn><mi>c</mi></math>, away from Earth. It launches a probe away from Earth, at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>50</mn><mi>c</mi></math> relative to the spaceship. An observer on the probe measures the length of the probe to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>0</mn><mo> </mo><mi mathvariant="normal">m</mi></math>.</p>
<p style="text-align: center;"><img 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57tk2fPnh3efffPhzStN954/UD+NYd4oqCmMigiavLWNFtpcLnz427vXEM+LXWP2juB6GVI61YMeSAexlzwiRvppT1otFMhRmrmvRsR8eOPPy7qp88++/tRpCgiFsU8KHFFxCBMTURiDJubg9p6y5qA33ghQjTwGd9pW6aGSCNNj++1B0VEJg8qIjKBzJCMIiIDxIqSiC5heiYujT9XVCxNLYAAbcnLL790eOml/87S40VdffHF/zq88srLWdIrANFBEdHxAmLgzTf/8OvQB0MSbIvAgkNs++ijv/0aJ43PXVEMYRCPIY50SOXtt/90+Prrf0ZyxX/WeEGu0ebiK0IFBsakyxbu7irAvQsTEaWvvfbK4Y9//L/Z8xYY1mD+w+3b/3t47bVXRw2JlAxbEZF4J3oT0ot8dxsiAqGAOCBE3IjXHc4gLoIjAschLpYeXon85n7WeEGu0ea5fvL4nwnge8aZa56opi/LIUDvVsyBmLMwFT0Q8bQGpSMt5km0EHYjIriY9/1FrwHOpEch/c02LvYch3gghIj44ot/HH/Hv1MigjTTwHGkF+Ij3Vfi9xovyDXaXKLva7WJOz4aaRpt6oJBAlMIcOFHkKaTKKO3a0y9irkQ6RoU9HBwHWhh+G03ImLMnT+CALHAH70GfSIi7XGggp4SEV1RgnhQREw5pYcfo4gYzqrlmDTaLcx+b9lHJZeNngJEQzf0iYJunPh9bjVM0m9hQrAiIrz9y9AEF3j+GIJARHz77b8UEffeSSiV/1URUb6P1rKQO7147p87S4MEhhI49/hw9FKcGpKI3jDq3ql6x+Oe7K89KCISD9LrwMTHNLD+gz0Rioi0Tvi9PgJxR5h2KddXCi1eiwDik16scyEmSiIE0iGPEK7Mp0i3d9NiH9eW2oMi4hcPMjyRioVwbAw/0CtB4JN4DmcEofI+7YkozyclWBRrSowZzy7Bbm1Yn8CYNoTeiOi1iB6KvmGQvlLEcX37atmmiEg8xSRI/uh9ICAg+I1oiCcsTomIdMJkHE/PhnMiEsArfR3TAKxkktlsTCCWyrYnYmNHVJL92DaEesV6ElwrxjxiTG9F7aJ2NyIC5576i14GehcYzoh4fGfCJEIihjlOiQgmbvL4JsdGXEXENi3G2AZgGyvNdS0CNPB0TY9p3NeyzXzKJDC2DaE3grb/1Vf/Z9RkSUVEmf7XqowExp5MGbOenFSNNk8urAeeJUDjjoA4Nbnt7MHu3C2BoW0I8xoQAsyLQERQz/g+dJ0ShzN2W8X2U/ChJ1NJRGq0uSR+LdiSNu7nJre1UFbLkJ/AkEmPCAZEAEI1jZ/WvXPrQKTH5C/Beik2P5yxHso2c6rxglyjzW3Wnm1KFXeD0bhvY4W51k4AgUBb0hdijk26zgM9EWm4tDAVw2v0YtQeFBG1e3Bh+2u8INdo88Ju3E3y+J7hi7Rx303hLWhWAogAhGg3xOPC6Wu9idMVEWxDKLC9bz4OQx4tTPRVRHRriL+vEajxglyjzdeg+2MSgXMN9qQEPWjXBBiKQADEkATDD4iKU/MY+kQEAOkZQ9imgoQ02UaatQdFRO0eXNj+Gi/INdq8sBubT54G2gmUzbt59QJSr2KSJBMmGX44deE/JSIwmmPS40mnld4yRcTq1bKuDOmyq23cThFRVx2bYy2NM408DXTcMc5Jz2MlkBKgfvHYJmtApD0JaZz4fk5EEIe0SINH/3//+9+dFCORXi2fiohaPLWRnajl2hSzImKjyrJytoiGMY/TrWye2TVAIIbIEAi0K+fCJRHBsaT329++eBQm3TkV59IueZ8iomTvFGCbIqIAJ2jCDQIxzjx0eeEbCbhBAhcIxNMV1LUQE3yeCpdERCx6Rnp9T3ecSrf07YqI0j20sX2KiI0dYPY3CAxp0G8c5AYJDCTAsANDuN0hMnoimHfD8Fnf0NkpEUFc0utOyERMpOtMDDSvuGiKiOJcUpZBqPHaHkNyOKOsOpTTmrg7vNS1nDNP09oPAS7s54bIEBjUQQQD8xvoUWAbIRURbEPsIjgQHtyMRbyUJtv6BEsap/TviojSPbSxfVTw2hpsRcTGlWaB7GlsabRp4GnoDRLITWDMEAO9C9xc0T4iHhAKfPI7/U6cPvHQtZ26zXE11m1FRNeb/r5GQBFxDYc/NiBAI4x4oC4OaZA3MNEsKycQ8xXOzXk4V0Qu/ogIbmD6hjrOHRv7ah2mU0SEB/3sJcCY3dSTojfBFTbaE7EC5JWyoHHmDo07NYMEliBA3erOV5iSTzqcMeV4jon6zpBJLUERUYunNrIzx4mxtumKiLWJL5Mfd2YIiKl3h8tYZaqtEIgeLnq5cvRw5WoruWmrqedNEdHKGbFQOXKdGAuZ15ssIoI7i3iyJNfnJ598fPjgg79mTzeXfS2lExMoW3mWvreiunFTAojTnHf8OdtKRA220ZaVHhQRpXtoQ/tqvaPnBDx1QeVEP7Xv0vbo9rwUz/0/L1A2l0Ntw2gbnqpmXQCBnCKigOIMNkERMRjV/iLWKiLOeWrOid4ij3Os3CcBCQwnMKdtGZ5LeTEVEeX5pBiL4k6yGIMyGDLnRFdEZHCASUigUQJz2paakSgiavbewrYzJoeQaCnMOdFhkXMMtSWulkUCeycwp22pmZ0iombvLWx7jWtEXEIy50RvUVRd4uV+CUhgGIE5bcuwHMqMpYgo0y9FWJXj2ekiCpIYMedER1T5tEAC068SkMCvBOa0Lb8mUuEXRUSFTlvL5BZPijllYs0CnxhYq/aZjwTqIjCnbamrpNetVURc5+GvXwiwchoLnrQWpp7o8KBnxiABCUhAAv8hoIj4Dwu/JQTotucNdK2FqSKCSZUuvdxabbA8EpDAXAKKiLkEGz2+xcc7cdVUEUEvhPMhGq3sFksCEphMQBExGV3bB7Y6iXCKiGB9CIcy2q7vlk4CEphGQBExjVvzR3HRbHES4RQRgaDyJVDNV3kLKAEJTCCgiJgArfVDePcETyK0GMaKCMSDvRAt1gTLJAEJ5CCgiMhBsbE0GPvn7rvFMEZE8EQGYorhDIMEJCABCdwkoIi4yWT3W1qdVIljh4oIemN4xBUWBglIQAIS6CegiOjnsuutrU6qxKlDRESskeEjnbs+DSy8BCQwgIAiYgCkvUWhC5878RbDJRHx+PHnxyEMeyBa9L5lkoAEchNQROQmWnl6ra/M2CciEEwxgZIhDOdAVF6JNV8CEliNgCJiNdR1ZMSdeMvd+IiImPNBORENbGN1TheTqqOOaqUEJFAOAUVEOb4owhIupi2viZCKCMSEvQ5FVDuNkIAEKiWgiKjUcUuZ7ZsqlyJruhKQgATaI6CIaM+nk0vU+nyIyWA8UAISkIAEegkoInqx7HMj8yGurh7us/CWWgISkIAERhNQRIxG1u4BLa8P0a7XLJkEJCCB7QgoIrZjX1TOPObIpMNW14coCrbGSEACEmiEgCKiEUfOLQaPN/JkhkECEpCABCQwlIAiYiipxuOxZgJzIgwSkIAEJCCBoQQUEUNJNR7PRzsbd7DFk4AEJLAAAUXEAlBrS5KhDFZuNEjgFIE33nj98P77fzm1+7j9s8/+fpxX8/33/z4bz50S2AMBzgPmmXFetBwUES17d2DZHMoYCGrH0YaIiB3jsegSuEFAEXEDiRtaJeBQRquezVcuRUQ+lqa0DwKKiH34efeldCgjfxX45JOPj92YdGXy9+67fz48e/bsmFHasLA94vQNFdAN+uabf/g1Dhfyvq7RND/ifPHFP64V6uuv/3m0IfIiX+xIQ5pG12bikS7HYWek8/bbfzqQdoTucAZxiRPbOY7ypMfEsX5KYG0CQ+ondZV6m54ffCdwnlG/43zg/EjrdpzrH330t2vx+N0NHJe2B33naPeYUn47nFGKJzayw6GMvOBpYLjghmj48ccfjw0IF09CNCw0PCEI2MZ+Go4IceFNG6W+bdHwRLxo7OL3t9/+69jIpWnzPbXxks3YRHxsThvASIcyEsK+ECghOGhogwfHkw52GSSwJYEh9ZPziPrK+Ukdjj8ERN/5kNbt9FwPYd93rg85R7fkdClvRcQlQo3vdygjr4O5YIZg6Es5GhYasDTEBTgurqTRjcPFmkYq7oSi8Ukv7KQZvQZ8J50+e9L0L9kcaXbTiYY0BEuUoSsi4neUl3RSURPb/ZTAmgRCRJyrnyEiuucYdZjzphvS7WPO9e65Rbps67YB3fxK+K2IKMELG9nAK79Z6tqQj0BcSLnAxsU+TT0alrgziX2xnePTwG/Sid6CVESkeaXHxHfumrp3S7GPxgmxQUjT6bOZOMTtNmjRwJ4TEX2NY5p32OOnBNYmQD28VD+jjqfn5alzFfujp41zL+J1z/U4L0kzvndFCmnVcp4oItauuQXlxwqVCAlDXgI0DtxpcwHnj4YqGqFoWOLCGzl3exmi8QoRwMU9eh7iQs8n+7tpRZqRV9jR95kORZyymfSmioi+u7WwO/IOe/2UwJoEuEhfqp9xHsb5i31928LuqNuce3H+dc/P9FyPOH3nZmwr/TxRRIT3d/b5/PkPB4YyfFfGso7nLiQuzjQm0Wh0G5bYHo0VF+1uAxd3LSEiiEtD073TiRJ148f2S59dm4mfU0TUcod1iZP76yZwSkSk9bNPMHTP1ZRC9ERw4Y943XM9zkvO3/ge53SaVi3fFRG1eCqznY8efXpgUqVheQLRmNBoxPduoxGCgN6GU3GiQYtjo2ei2xVKzwcXfQLfu2KE7Wzr2x40wgbsIkwVERzXvZPCJudEBGk/tyIQYuFc/YxzLs6DsPXUecV2/ghxDsX5GsfGuc5+wqm0Lp2jkd7Wn4qIrT2wUf537tw+PH36dKPc2802TnzuMCJwweRiyrZoWNIeBBoq9qcX1miMIh3isI3jUtEQabOfEA1UNHr0KnAMDWaEuFtChBAu2UycqSKCvLExGmq+sy3yDpv8lMDaBDgnLtXPUyIizqvuuZjW7XPnenpcpHXuHF2bzZj8FBFjaDUS17UhlnMkF8u4SNOgRCMVdx3RsNBgcPGOOHHRD8uIl+7nO3H67lq404l0uNh306IhjIs38UgrRAf5XbKZOFNFBMelPLAjWERZ/ZTAFgQ4By/Vz1MiAnu5+KfnKHU7Pa/iXOd8TON1z0/SunSObsFnaJ6KiKGkGorHExlOqNzGoWnDso0F6+UajfR6OZqTBIYTsH4OZ3UupiLiHJ0G98WEygaLVkWRFBFVuEkjd0BAEZHHyYqIPByrSYXJlEyqNGxDQBGxDXdzlUCXgCKiS2Tab0XENG5VHsXjnIyJ0xthkIAEJCABCcwloIiYS7Ci432ssyJnaaoEJCCBCggoIipwUg4T6YXwPRk5SJqGBCQgAQkEAUVEkGj8k14Ilrk2SEACEpCABHIRUETkIllwOtEL8d133xVspaZJQAISkEBtBBQRtXlsgr30Qvi2zgngPEQCEpCABM4SUEScxVP/Tnsh6vehJZCABCRQKgFFRKmeyWSXvRCZQJqMBCQgAQncIKCIuIGknQ32QrTjS0siAQlIoEQCiogSvZLJJteFyATSZCQgAQlIoJeAIqIXS/0bWZXS1Snr96MlkIAEJFAyAUVEyd6ZYRvvyLi6ejgjBQ+VgAQkIAEJnCegiDjPp8q9rAfB6pTMiTBIQAISkIAEliKgiFiK7Ibp3r371uHx4883tMCsJSABCUhgDwQUEY15GfGAiDBIQAISkIAEliagiFia8Irp+0jnirDNSgISkIAEDoqIhioBkyn5M0hAAhKQgATWIKCIWIPyCnk4mXIFyGYhAQlIQALXCCgiruGo8wfDGHfu3D589dWXdRZAqyUgAQlIoEoCiogq3XbdaNaD8C2d15n4SwISkIAEliegiFie8aI5xDAGK1QaJCABCUhAAmsSUESsSTtzXjGM4ZoQmcGanAQkIAEJDCKgiBiEqcxIDmOU6RetkoAEJLAXAoqISj395Mk3Lm1dqe80WwISkEArBL2N9wsAAAUvSURBVBQRFXqS+Q+8GwMhYZCABCQgAQlsRUARsRX5GfnyJIZv6JwB0EMlIAEJSCALAUVEFozrJfLo0ae+G2M93OYkAQlIQAJnCCgizsApbVfMg/BxztI8oz0SkIAE9klAEVGJ350HUYmjNFMCEpDAjggoIipwNutB8HpvhjIMEpCABCQggVIIKCJK8cQZO+7ff+/An0ECEpCABCRQEgFFREne6LGFpzDohaA3wiABCUhAAhIoiYAioiRvdGzhrZysB/H06dPOHn9KQAISkIAEtiegiNjeB70W8GKtW7deUED00nGjBCQgAQmUQEARUYIXOjbQ80APBD0RBglIQAISkECpBBQRhXlGAVGYQzRHAhKQgAROElBEnESz/o54lPPBgw/Xz9wcJSABCUhAAiMJKCJGAlsqugJiKbKmKwEJSEACSxFQRCxFdkS6CogRsIwqAQlIQALFEFBEbOwKBcTGDjB7CUhAAhKYTEARMRnd/AMVEPMZmoIEJCABCWxHQBGxEXsFxEbgzVYCEpCABLIRUERkQzk8IR7jZClrn8IYzsyYEpCABCRQHgFFxMo+iXUgFBArgzc7CUhAAhLITkARkR3p6QRDQPhK79OM3CMBCUhAAvUQUESs5CuWsOZdGC5lvRJws5GABCQggcUJKCIWR3w40PPAuzB4qZZBAhKQgAQk0AoBRcSCnuQJDOY+3Llz27dxLsjZpCUgAQlIYBsCioiFuD9//sPxCQyewkBMGCQgAQlIQAKtEVBELODRJ0++OQ5fXF09XCB1k5SABCQgAQmUQUARkdkPCAfmPziBMjNYk5OABCQggeIIKCIyuSQdvuBRToMEJCABCUigdQKKiAwejuELJlE6/yEDUJOQgAQkIIEqCCgiZrgJwXD//nvH4QuEhEECEpCABCSwJwKKiInejt6He/fesfdhIkMPk4AEJCCBugkoIkb6L+19ePz485FHG10CEpCABCTQDgFFxAhfIhp48oIhDOc+jABnVAlIQAISaJKAImKAW1mumkWjWHnSuQ8DgBlFAhKQgAR2QUARccbNPLbJExe8OIv3X9j7cAaWuyQgAQlIYHcEFBE9LkcsxEuzGLpATBgkIAEJSEACErhOQBGR8EjFA09d+NbNBI5fJSABCUhAAh0CiojD4ThMET0PzH1QPHRqiT8lIAEJSEACPQR2LSK6PQ++76KnhrhJAhKQgAQkcILALkVETJjkcU2HLU7UDDdLQAISkIAELhDYlYjg8UwmSvK0BU9d+KKsC7XD3RKQgAQkIIEzBJoXEfQ6MN+BNR7447tPW5ypEe6SgAQkIAEJDCTQpIhgrgOrSzJJkl4Heh9cJGpgjTCaBCQgAQlIYCCBZkQEvQsIhxiuQEAwURJBYZCABCQgAQlIID+BqkUEj2JeXT281uOAkHC4In9FMUUJSEACEpBAl0BVIgLRwJwGnqhgmII5DkyQZKjCHoeua/0tAQlIQAISWJZAsSICwUCvQtrTEKKBYQp7G5atGKYuAQlIQAISuERgMxFBzwFCIXoXEAv0MCAUopeB+Q30PNjTcMmN7peABCQgAQmsTyC7iKD3gAs/wwyIgvQvnpZAJPDHb/YjIEIsICoMEpCABCQgAQmUTyC7iCi/yFooAQlIQAISkEAOAoqIHBRNQwISkIAEJLBDAoqIHTrdIktAAhKQgARyEFBE5KBoGhKQgAQkIIEdElBE7NDpFlkCEpCABCSQg4AiIgdF05CABCQgAQnskIAiYodOt8gSkIAEJCCBHAT+H5rdx/5w+c8rAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean transformations assume.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the length of the probe as measured by an observer in the spaceship.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain which of the lengths is the proper length.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the probe in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>, relative to Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Two rockets, A and B, are moving towards each other on the same path. From the frame of reference of the Earth, an observer measures the speed of A to be 0.6<em>c</em> and the speed of B to be 0.4<em>c</em>. According to the observer on Earth, the distance between A and B is 6.0 x 10<sup>8</sup> m.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define frame of reference.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to the observer on Earth, the time taken for A and B to meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the terms in the formula.</p>
<p><em>u′</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}">
<mfrac>
<mrow>
<mi>u</mi>
<mo>−</mo>
<mi>v</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mi>u</mi>
<mi>v</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, according to an observer in A, the velocity of B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, according to an observer in A, the time taken for B to meet A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, without further calculation, how the time taken for A to meet B, according to an observer in B, compares with the time taken for the same event according to an observer in A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Muons are created in the upper atmosphere of the Earth at an altitude of 10 km above the surface. The muons travel vertically down at a speed of 0.995<em>c </em>with respect to the Earth. When measured at rest the average lifetime of the muons is 2.1 μs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer on Earth watches rocket A travel away from Earth at a speed of 0.80<em>c</em>. The spacetime diagram shows the worldline of rocket A in the frame of reference of the Earth observer who is at rest at <em>x </em>= 0.</p>
<p style="text-align: left;"><img src="data:image/png;base64,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"></p>
<p>Another rocket, B, departs from the same location as A but later than A at <em>ct </em>= 1.2 km according to the Earth observer. Rocket B travels at a constant speed of 0.60<em>c </em>in the opposite direction to A according to the Earth observer.</p>
</div>
<div class="specification">
<p>Rocket A and rocket B both emit a flash of light that are received simultaneously by the Earth observer. Rocket A emits the flash of light at a time coordinate <em>ct </em>= 1.8 km according to the Earth observer.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, showing your working on the spacetime diagram, the value of <em>ct </em>according to the Earth observer at which the rocket B emitted its flash of light.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of rocket B relative to rocket A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Observer A detects the creation (event 1) and decay (event 2) of a nuclear particle. After creation, the particle moves at a constant speed relative to A. As measured by A, the distance between the events is 15 m and the time between the events is 9.0 × 10<sup>–8</sup> s.</p>
<p>Observer B moves with the particle.</p>
<p>For event 1 and event 2,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by the statement that the spacetime interval is an invariant quantity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>calculate the spacetime interval.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>determine the time between them according to observer B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the observed times are different for A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by proper length.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the axes for two inertial reference frames. Frame S represents the ground and frame S′ is a box that moves to the right relative to S with speed <em>v</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>When the origins of the two frames coincide all clocks show zero. At that instant a beam of light of speed <em>c</em> is emitted from the left wall of the box towards the right wall. The box has proper length <em>L</em>. Consider the event E = light arrives at the right wall of the box.</p>
<p><br>Using <strong>Galilean</strong> relativity,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a reference frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>explain why the time coordinate of E in frame S is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = \frac{L}{c}">
<mi>t</mi>
<mo>=</mo>
<mfrac>
<mi>L</mi>
<mi>c</mi>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>hence show that the space coordinate of E in frame S is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = L + \frac{{vL}}{c}">
<mi>x</mi>
<mo>=</mo>
<mi>L</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mi>L</mi>
</mrow>
<mi>c</mi>
</mfrac>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket of proper length 120 m moves to the right with speed 0.82<em>c</em> relative to the ground.</p>
<p style="text-align: center;"><img 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"></p>
<p>A probe is released from the back of the rocket at speed 0.40<em>c</em> relative to the rocket.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the probe relative to the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The spacetime diagram shows the axes of an inertial reference frame S and the axes of a second inertial reference frame S′ that moves relative to S with speed 0.745<em>c</em>. When clocks in both frames show zero the origins of the two frames coincide.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Event E has coordinates <em>x</em> = 1 m and <em>ct</em> = 0 in frame S. Show that in frame S′ the space coordinate and time coordinate of event E are</p>
</div>
<div class="specification">
<p>A rod at rest in frame S has proper length 1.0 m. At <em>t</em> = 0 the left-hand end of the rod is at <em>x</em> = 0 and the right-hand end is at <em>x</em> = 1.0 m.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><em>x</em>′ = 1.5 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><em>ct</em>′ = –1.1 m.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the letter P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label, on the diagram, the event that has coordinates <em>x</em>′ = 1.0 m and <em>ct</em>′ = 0. Label this event with the letter Q.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the length of the<br>rod to be less than 1.0 m.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the motion of the electrons in a metal wire carrying an electric current as seen by an observer X at rest with respect to the wire. The distance between adjacent positive charges is <em>d</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-11_om_06.22.52.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/03"></p>
</div>
<div class="specification">
<p>Observer Y is at rest with respect to the electrons.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the field around the wire according to observer X is electric, magnetic or a combination of both.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss the change in <em>d </em>according to observer Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Rocket A and rocket B are travelling in opposite directions from the Earth along the same straight line.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.33.49.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/03"></p>
<p>In the reference frame of the Earth, the speed of rocket A is 0.75<em>c </em>and the speed of rocket B is 0.50<em>c</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>When a spaceship passes the Earth, an observer on the Earth and an observer on the spaceship both start clocks. The initial time on both clocks is 12 midnight. The spaceship is travelling at a constant velocity with <em>γ</em> = 1.25. A space station is stationary relative to the Earth and carries clocks that also read Earth time.</p>
</div>
<div class="specification">
<p>Some of the radio signal is reflected at the surface of the Earth and this reflected signal is later detected at the spaceship. The detection of this signal is event B. The spacetime diagram is shown for the Earth, showing the space station and the spaceship. Both axes are drawn to the same scale.</p>
<p style="text-align: left;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the spaceship relative to the Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Construct event A and event B on the spacetime diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The speed of a spaceship is measured to be 0.50<em>c</em> by an observer at rest in the Earth’s reference frame.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Define an <em>inertial reference frame.</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">As the spaceship passes the Earth it emits a flash of light that travels in the same direction as the spaceship with speed <em>c</em> as measured by an observer on the spaceship. Calculate, according to the Galilean transformation, the speed of the light in the Earth’s reference frame.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A spaceship moves away from the Earth in the direction of a nearby planet. An observer on the Earth determines the planet is 4 ly from the Earth. The spacetime diagram for the Earth’s reference frame shows the worldline of the spaceship. Assume the clock on the Earth, the clock on the planet, and the clock on the spaceship were all synchronized when<em> ct</em> = 0.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80<em>c</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label, with the letter E, the event of the spaceship going past the planet.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine, according to an observer on the spaceship as the spaceship passes the planet, the time shown by the clock on the spaceship.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine, according to an observer on the spaceship as the spaceship passes the planet, the time shown by the clock on the planet.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to Earth at a speed of 0.80<em>c</em> relative to Earth. Suggest, for this situation, how the twin paradox arises and how it is resolved.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A train of proper length 85 m moves with speed 0.60<em>c</em> relative to a stationary observer on a platform.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Define <em>proper length</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">In the reference frame of the train a ball travels with speed 0.50<em>c</em> from the back to the front of the train, as the train passes the platform. Calculate the time taken for the ball to reach the front of the train in the reference frame of the train.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">In the reference frame of the train a ball travels with speed 0.50<em>c</em> from the back to the front of the train, as the train passes the platform. Calculate the time taken for the ball to reach the front of the train in the reference frame of the platform.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">bii.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket moving with speed v relative to the ground emits a flash of light in the backward direction.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">An observer in the rocket measures the speed of the flash of light to be <em>c</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <strong>speed</strong> of the flash of light according to an observer on the ground using Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <strong>speed</strong> of the flash of light according to an observer on the ground using Maxwell’s theory of electromagnetism.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <strong>speed</strong> of the flash of light according to an observer on the ground using Einstein’s theory of relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows space and time axes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <em>ct</em> for an observer at rest with respect to a galaxy. A spacecraft moving through the galaxy has space and time axes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>′ and <em>ct</em>′.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">A rocket is launched towards the right from the spacecraft when it is at the origin of the axes. This is labelled event 1 on the spacetime diagram. Event 2 is an asteroid exploding at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = 100 ly and <em>ct</em> = 20 ly.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot, on the axes, the point corresponding to event 2.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly<sup>2</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart. Determine, according to the spacecraft observer, the time between events 1 and 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, using the diagram, the speed of the spacecraft relative to the galaxy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A long straight current-carrying wire is at rest in a laboratory. A negatively-charged particle P outside the wire moves parallel to the current with constant velocity<em> v</em> relative to the laboratory.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">In the reference frame of the laboratory the particle P experiences a repulsive force away from the wire.</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">One of the two postulates of special relativity states that the speed of light in a vacuum is the same for all observers in inertial reference frames. State the other postulate of special relativity.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">State the nature of the force on the particle P in the reference frame of the laboratory.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain how the force in part (b)(ii) arises.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The velocity of P is 0.30<em>c</em> relative to the laboratory. A second particle Q moves at a velocity of 0.80<em>c</em> relative to the laboratory.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Calculate the speed of Q relative to P.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iv).</div>
</div>
<br><hr><br><div class="specification">
<p>Muons are created at a height of 3230 m above the Earth’s surface. The muons move vertically downward at a speed of 0.980 c relative to the Earth’s surface. The gamma factor for this speed is 5.00. The half-life of a muon in its rest frame is 2.20 μs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The spacetime diagram is in the reference frame of an observer O on Earth. Observer O and spaceship A are at the origin of the spacetime diagram when time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>t</mi><mo>'</mo><mo>=</mo><mn>0</mn></math>. The worldline for spaceship A is shown.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="specification">
<p>Event E is the emission of a flash of light. Observer O sees light from the flash when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>9</mn></math> years and calculates that event E is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>ly</mi></math> away, in the positive <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> direction.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> the velocity of spaceship A relative to observer O.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>'</mo></math> axis for the reference frame of spaceship A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the event E on the spacetime diagram and label it E.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time, according to spaceship A, when light from event E was observed on spaceship A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A train is moving across a bridge with a speed <em>v</em> = 0.40<em>c</em>. Observer A is at rest in the train. Observer B is at rest with respect to the bridge.</span></p>
<p><span style="background-color: #ffffff;">The length of the bridge<em> L</em><sub>B</sub> according to observer B is 2.0 km.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">According to observer B, two lamps at opposite ends of the bridge are turned on simultaneously as observer A crosses the bridge. Event X is the lamp at one end of the bridge turning on. Event Y is the lamp at the other end of the bridge turning on.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img 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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Events X and Y are shown on the spacetime diagram. The space and time axes of the reference frame for observer B are <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></em> and <em>ct</em>. The line labelled <em>ct'</em> is the worldline of observer A.</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><img 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hsgQHO8AahMCYGaBLSkLvHH+oqUzN27XjuIFyV2iVMbPevu0WZfWtZbfZ9ap605j0GgdwJaHeWV495Xnfi6JqAldUnA1qIrc/eu1w7iRYld4tRGz7p7tNmXlvVW36fWaWvOYxDonYBWR2mOe1914uuagJbUJQFbi67M3bN+2UG8CLFLjMtGz7p7tNmflvVW36fWLVt3HodAzwS0Okpz3POKE1v3BLSkLgnaWnRl7p71yw7iRYhdYlw2etbdo83+tKy3+j61btm68zgEeiag1VGa455XnNi6J6AldUnQ1qIrc/esX/xGPIlZxp5jlxiXjZ7YPdrsT8t6q+9T65atO49DoGcCWh2lOe55xYmtewJaUpcEbS26Mnev+lUH8XqPXeJbNXrW3aPNPrWst/o+tW7V2vMcBHoloNVRmuNeV5u4QhDQkrokcGvRlbl71a86iNd77BLfqtGz7h5t9qllvdX3qXWr1p7nINArAa2O0hz3utrEFYKAltQlgVuLrszdo37dQbyeY5fY1o2edfdos18t662+T61bt/48D4EeCWh1lOa4x5UmpjAEtKQuCd5adGXuHvXrDuL1HLvEtm70rLtHm/1qWW/1fWrduvXneQj0SECrozTHPa40MYUhoCV1SfDWoitz96hfdxCv59gltnWjZ9092uxXy3qr71Pr1q0/z0OgRwJaHaU57nGliSkMAS2pS4K3Fl2Zuzd9yUG8XmOXuEpGz7p7tNm3lvVW36fWlewBroFAbwS0Okpz3NsqE08oAlpSlwCwFl2Zuzd9yUG8XmOXuEpGz7p7tNm3lvVW36fWlewBroFAbwS0Okpz3NsqE08oAlpSlwCwFl2Zuyd96UG8HmOXmEpHz7p7tNm/lvVW36fWle4DroNATwS0Okpz3NMKE0s4AlpSl0CwFl2Zuyd96UG8HmOXmEpHz7p7tNm/lvVW36fWle4DroNATwS0Okpz3NMKE0s4AlpSl0CwFl2Zuyd96UG8HmOXmEpHz7p7tNm/lvVW36fWle4DroNATwS0Okpz3NMKE0soArlw5qTOI782Bk+fPk03b96EH3uouz0Q6o8hwULAQYDm2AEPKQS2kYCW1CV+Wl+Rkrl70Y85iNdb7BLPmNGz7h5t9rFlvdX3qXVj9gLXQqAXAlod5ZXjXlaXOEIS0JK6BIS16MrcPejHHsTrKXaJZezoWXePNvvZst7q+9S6sfuB6yHQAwGtjtIc97CyxBCWgJbUJTCsRVfm7kE/9iBeT7FLLGNHz7p7tNnPlvVW36fWjd0PXA+BHghodZTmuIeVJYawBLSkLoFhLboydw/6sQfxeopdYhk7etbdo81+tqy3+j61bux+4HoI9EBAq6M0xz2sLDGEJaAldQkMa9GVuVvX54N4t27dknBGja3H7vG/ljYvkMd2bb3V96l1oxKBiyHQCQGtjtIcd7K4hBGTgJbUJSSsRVfmbl1/79699OTJEwln1Nh67B7/a2nzAnls19ZbfZ9aNyoRuBgCnRDQ6ijNcSeLSxgxCWhJXULCWnRl7pb1+SBe/vi2ly9fSjijxpZjz4F6/K+l9fpdW2/lNrVuVCJwMQQ6IaDVUZrjThaXMGIS0JK6hIS16MrcLevzQbw7d+5IKKPHlmPPwXr8r6X1+l1bb+U2tW50MiCAQAcEtDpKc9zBwhJCXAJaUpfQsBZdmbtlfT6I9+jRIwll9Nhy7DlYj/+1tF6/a+ut3KbWjU4GBBDogIBWR2mOO1hYQohLQEvqEhrWoitzt6r/8ssvzw/iefz3aDO/lvUe3z3aqNyszKw6yW9GCEQioNVRmuNIO4BYuyOgJXVJkN7i2apevhHP479Hm9emZb3Hd482KjcrM6uu5G8H10CgNwJaHaU57m2ViScUAS2pSwB4i2eL+uE34nn892jz2rSs9/ju0UblZmVm1ZX87eAaCPRGQKujNMe9rTLxhCKgJXUJAG/xbFE//EY8j/8ebV6blvUe3z3aqNyszKy6kr8dXAOB3ghodZTmuLdVJp5QBLSkLgHgLZ4t6offiOfx36PNa9Oy3uO7RxuVm5WZVVfyt4NrINAbAa2O0hz3tsrEE4qAltQlALzFszW9HMQTNh7/Pdpsv2W9x3ePNio3KzOrTvKDEQKRCGh1lOY40g4g1q4I5AKYkzqP/K5mkL8R78GDB3Bir4TZA139sSMYCGyQAM3xBuEyNQRqENCSusQP7ytLLemHB/GEjcd/jzbbb1nv8d2jjcrNysyqk/xghEAkAlod5ZXjSDuAWLsjoCV1SZDe4tmSfngQT9h4/Pdos/2W9R7fPdqo3KzMrDrJD0YIRCKg1VGa40g7gFi7I6AldUmQ3uLZkn54EE/YePz3aLP9lvUe3z3aqNyszKw6yQ9GCEQioNVRmuNIO4BYuyOgJXVJkN7i2Yp+8SCesPH479Fm+y3rPb57tFG5WZlZdZIfjBCIRECrozTHkXYAsXZHQEvqkiC9xbMVvXwj3iITj/8ebfajZb3Hd482KjcrM6tuMU+4D4EIBLQ6SnMcYeWJsVsCWlKXBOstni3otYN4wsbjv0eb7bes9/ju0UblZmVm1Ul+MEIgEgGtjtIcR9oBxNodAS2pS4L0Fs8W9NpBPGHj8d+jzfZb1nt892ijcrMys+okPxghEImAVkdpjiPtAGLtjoCW1CVBeotnC3rtIJ6w8fjv0Wb7Les9vnu0UblZmVl1kh+MEIhEQKujNMeRdgCxdkdAS+qSIL3Fc9v1yw7iCRuP/x5ttt+y3uO7RxuVm5WZVSf5wQiBSAS0OkpzHGkHEGt3BLSkLgnSWzy3Xb/sIJ6w8fjv0Wb7Les9vnu0UblZmVl1kh+MEIhEQKujNMeRdgCxdkdAS+qSIL3Fc5v1qw7iCRuP/x5ttt+y3uO7RxuVm5WZVSf5wQiBSAS0OkpzHGkHEGt3BLSkLgnSWzy3Wb/qIJ6w8fjv0Wb7Les9vnu0UblZmVl1kh+MEIhEQKujNMeRdgCxdkdAS+qSIL3Fc5v1qw7iCRuP/x5ttt+y3uO7RxuVm5WZVSf5wQiBSAS0OkpzHGkHEGt3BLSkLgnSWzy3Vb/uIJ6w8fjv0Wb7Les9vnu0UblZmVl1kh+MEIhEQKujNMeRdgCxdkUgF8Cc1Hnk9w2De/fupQcPHsCDPRF+D3T1x45gILBBAjTHG4TL1BCoQUBL6hI/vK8sbaO+5CCesPH479Fm+y3rPb57tFG5WZlZdZIfjBCIRECro7xyHGkHEGt3BLSkLgnSWzy3UV9yEE/YePz3aLP9lvUe3z3aqNyszKw6yQ9GCEQioNVRmuNIO4BYuyOgJXVJkN7iuY36koN4wsbjv0eb7bes9/ju0UblZmVm1Ul+MEIgEgGtjtIcR9oBxNodAS2pS4L0Fs9t05cexBM2Hv892my/Zb3Hd482KjcrM6tO8oMRApEIaHWU5jjSDiDW7ghoSV0SpLd4bpt+3TfiLTLx+O/RZj9a1nt892ijcrMys+oW84T7EIhAQKujNMcRVp4YuyWgJXVJsN7iuU36MQfxhI3Hf482229Z7/Hdo43KzcrMqpP8YIRAJAJaHaU5jrQDiLU7AlpSlwTpLZ7bpB9zEE/YePz3aLP9lvUe3z3aqNyszKw6yQ9GCEQioNVRmuNIO4BYuyOgJXVJkN7iuU36MQfxhI3Hf482229Z7/Hdo43KzcrMqpP8YIRAJAJaHaU5jrQDiHVrCZydPEuf7N0+/1KPnKiznb30ydFJOlvjsZbUayTnT3uL57boxx7EEzYe/z3abL9lvcd3jzYqNyszq07ygxECkQhodZTmONIOINbtJHD6LO3vzNN89+P07OR1SulVev74bprPvpf2j75a6bOW1CsFF096i+e26McexBM2Hv892my/Zb3Hd482KjcrM6tO8oMRApEIaHWU5jjSDiDWrSTwzdF+ujH7dto7/NU7/745Svs3Zmm+d5hevXv0yi0tqa9cpDzgLZ7boLccxBMUHv892my/Zb3Hd482KjcrM6tO8oMRApEIaHWU5jjSDiDWLSRwlk6P/yUdHPxTOjp/1fjCxVeHaW9Oc7xswXLxtxzEk/k8zYNHm+23rPf47tFG5WZlZtVJfjBCIBIBmuNIq02sDRN4nV4cfJDms/fS3YNfrnzfsZbUJYF7i+c26C0H8YSNx3+PNttvWe/x3aONys3KzKqT/GCEQCQCWh3lleNIO4BYGyDwOp0cfph2ZrM03/0kPT9dfSRPS+qSIL3Fs7b+6dOn6datWyWhqtd4/PdoszMt6z2+e7RRuVmZWXVqsvAgBDonoNVRmuPOF53wWiLwKh0f3C9ujHNkWlKXROwtnrX19+7dS0+ePCkJVb3G479Hm51pWe/x3aONys3KzKpTk4UHIdA5Aa2O0hx3vuiE1woB+YSKsleMc1S5AOakzmOk388//zzdvHkzffbZZ6HijrTGxOrP6Vb+8uEnBGoToDmuvQLYh4BKQBrjedrZO0jHa95KMZxCS+rh88tu5+bD81NTnw/i3blzx+P+eVNtnaBm7NnnmvY9tj3a2nF77Vtjn1pnzQl0EGiZgFZHeeW45RXF9w4InKXTo4dv3kpx9yC9WP0W4yvxakl95SLlAWvRlalq6vNBvEePHokrptHjv0ebnW1Z7/Hdo43KzcrMqjMlEyIINE5Aq6M0x40vKu63TuA0He3vvPtmvPzteMPf3YN0siJELalXXP72KW/xrKWXb8SrZT8DrGm7tn1P7B5t7bi99q2xT63LcfIDgWgEtDpKcxxtFxBvVwS0pC4J0Fp0Ze5aevlGvFr2c/w1bde274ndo60dt9e+NfapdTlOfiAQjYBWR2mOo+0C4u2KgJbUJQFai67MXUM//Ea8GvZrxi6289hq7DX9bpWblZlVN9xn3IZAFAJaHaU5jrL6xNklAS2pSwL1Fs8a+uE34tWwL1xr2s4+1LTvse3R1o7ba98a+9Q62eOMEIhEQKujNMeRdgCxdkdAS+qSIK1FV+auoR9+I14N+zVjF9t5bDX2mn63ys3KzKob7jNuQyAKAa2O0hxHWX3i7JKAltQlgXqL59R6OYgnsU1tX+zmsabt2vY9sXu0teP22rfGPrUux8kPBKIR0OoozXG0XUC8XRHQkrokQGvRlbmn1stBvFr2xW4ep459aLu2fU/sHm3tuL32rbFPrVvca9yHQAQCWh2lOY6w8sTYLQEtqUuCtRZdmXtK/fAgXg37YlPGKWMXm8Oxpn2PbY82x9+y3ur71LrhPuM2BKIQ0OoozXGU1SfOLgloSV0SqLXoytxT6ocH8WrYF5syThm72ByONe17bHu0Of6W9Vbfp9YN9xm3IRCFgFZHaY6jrD5xdklAS+qSQK1FV+aeUj88iFfDvtiUccrYxeZwrGnfY9ujzfG3rLf6PrVuuM+4DYEoBLQ6SnMcZfWJszsCuXDmpM5jr79Pnz5NN2/e7Da+XteNuOrnZHd/8AgIAhsiQHO8IbBMC4FaBLSkLvElNy+en6n0iwfxxOep7Iu94VjTdvajpn2PbY+2dtxe+9bYp9YN9zm3IRCFgFZHeeU4yuoTZ5cEtKQuCdRadGXuKfTaQbwp7YutxXGK2BdtDu/XtO+x7dHm+FvWW32fWjfcZ9yGQBQCWh2lOY6y+sTZJQEtqUsCtRZdmXsKvXYQb0r7YmtxnCL2RZvD+zXte2x7tDn+lvVW36fWDfcZtyEQhYBWR2mOo6w+cXZJQEvqkkCtRVfmnkKvHcSb0r7YWhyniH3R5vB+Tfse2x5tjr9lvdX3qXXDfcZtCEQhoNVRmuMoq0+cXRLQkrokUGvRlbk3rV/8RjyxK+Om7YsdbaxpO/tT077HtkdbO26vfWvsU+u0/c5jEOidgFZHaY57X3Xi65qAltQlAVuLrsy9af2yg3hT2Rc72rjp2DWbw8dq2vfY9mhz/C3rrb5PrRvuM25DIAoBrY7SHEdZfeLskoCW1CWBWouuzL1J/aqDeFPYFxvLxk3Gvszm8PGa9j22Pdocf8t6qyBRu3oAACAASURBVO9T64b7jNsQiEJAq6M0x1FWnzi7JKAldUmg1qIrc29Sv+og3hT2xcaycZOxL7M5fLymfY9tjzbH37Le6vvUuuE+4zYEohDQ6ijNcZTVJ84uCWhJXRKotejK3JvUrzqIN4V9sbFs3GTsy2wOH69p32Pbo83xt6y3+j61brjPuA2BKAS0OkpzHGX1ibNLAlpSlwRqLboy96b06w7ibdq+zL9q3FTsq2wOn6tp32Pbo83xt6y3+j61brjPuA2BKAS0OkpzHGX1ibNLAlpSlwRqLboy96b06w7ibdq+zL9q3FTsq2wOn6tp32Pbo83xt6y3+j61brjPuA2BKAS0OkpzHGX1ibNLAlpSlwRqLboy9yb0JQfxNmlf5l43biL2dTaHz9e077Ht0eb4W9ZbfZ9aN9xn3IZAFAJaHaU5jrL6xNklAS2pSwK1Fl2ZexP6koN4m7Qvc68bNxH7OpvD52va99j2aHP8Leutvk+tG+4zbkMgCgGtjtIcR1l94uySgJbUJYFai67MvQl9yUG8TdqXudeNm4h9nc3h8zXte2x7tDn+lvVW36fWDfcZtyEQhYBWR2mOo6w+cXZJQEvqkkCtRVfmvm596UG8TdmXeUvG6469xObwmpr2PbY92hx/y3qr71PrhvuM2xCIQkCrozTHUVafOLsjkAtnTuo8tv5779699ODBg+bjaH0d8L/9XJI17O4PHgFBYEMEaI43BJZpIVCLgJbUJb7kAur5uU79mIN44vN12pc5S8eatrOPNe17bHu0teP22rfGPrWuNAe4DgI9EdDqKK8c97TCxBKOgJbUJRCsRVfmvk79mIN4m7Avc5aO1xl7qc3hdTXte2x7tDn+lvVW36fWDfcZtyEQhYBWR2mOo6w+cXZJQEvqkkCtRVfmvk79mIN4m7Avc5aO1xl7qc3hdTXte2x7tDn+lvVW36fWDfcZtyEQhYBWR2mOo6w+cXZJQEvqkkCtRVfmvi792IN4121f5hszXlfsY2wOr61p32Pbo83xt6y3+j61brjPuA2BKAS0OkpzHGX1ibNLAlpSlwRqLboy93XpS78RT+zKeF32Zb4xY03b2c+a9j22PdracXvtW2OfWjcmD7gWAr0Q0OoozXEvq0scIQloSV0Cwlp0Ze7r0FsO4l2nfZlr7HgdsY+1Oby+pn2PbY82x9+y3ur71LrhPuM2BKIQ0OoozXGU1SfOLgloSV0SqLXoytzXobccxLtO+zLX2PE6Yh9rc3h9Tfse2x5tjr9lvdX3qXXDfcZtCEQhoNVRmuMoq0+cXRLQkrokUGvRlbmvQ285iHed9mWuseN1xD7W5vD6mvY9tj3aHH/LeqvvU+uG+4zbEIhCQKujNMdRVp84uySgJXVJoNaiK3N79U+fPk23bt2S6UaPXvsevUebA21Z7/Hdo43KzcrMqhudiAgg0AEBrY7SHHewsIQQl4CW1CU0vMXTq8/fiPfkyZMSV9VrvPY9eo82B9Oy3uO7RxuVm5WZVacmGw9CoHMCWh2lOe580QmvbwJaUpdE7C2eHn0+iHfz5s308uXLElfVazz284QevUfrtV1b74ndo60dt9e+NfapdTlOfiAQjYBWR2mOo+0C4u2KgJbUJQFai67M7dHng3h37tyRqUyjx3426NF7tF7btfWe2D3a2nF77Vtjn1qX4+QHAtEIaHWU5jjaLiDerghoSV0SoLXoytwefT6I9+jRI5nKNHrsZ4MevUfrtV1b74ndo60dt9e+NfapdTlOfiAQjYBWR2mOo+0C4u2KgJbUJQFai67MbdXLN+JZ9V7716Fv2fccv8f/Wlqv37X1Vm5T6yQ/GCEQiYBWR2mOI+0AYu2KQC6cOanz2MpvPoj34MGDZvxthSt+tpMDU61VV3/sCAYCGyRAc7xBuEwNgRoEtKQu8SMXaM+PRT/8RjyLfuhvTX1N25lBTfse2x5t7bi99q2xT60b5hi3IRCFgFZHeeU4yuoTZ5cEtKQuCdRadGVui374jXgWvdjOY019Tdstxw634Q4uu21lZtWVecVVEOiLgFZHaY77WmOiCUZAS+oSBN7iadEPvxHPoh/GVVNf03ZmUNO+x7ZHWztur31r7FPrhjnGbQhEIaDVUZrjKKtPnF0S0JK6JFBr0ZW5x+rlIJ5VLzoZx9oXnYwevUeb7bes9/ju0UblZmVm1Ul+MEIgEgGtjtIcR9oBxNodAS2pS4L0Fs+x+o8++ujSN+KN1S/GVFNf03bmUNO+x7ZHWztur31r7FPrFvOM+xCIQECrozTHEVaeGLsloCV1SbDWoitzj9EPD+JZ9KIZjmPsD3Vy26P3aLP9lvUe3z3aqNyszKw6yQ9GCEQioNVRmuNIO4BYuyOgJXVJkN7iOUY/PIgnvo3Ri2Y41tTXtJ0Z1LTvse3R1o7ba98a+9S6YY5xGwJRCGh1lOY4yuoTZ5cEtKQuCdRadGXuMfrhQTyLXjTDcYz9oU5ue/Qebbbfst7ju0cblZuVmVUn+cEIgUgEtDpKcxxpBxBrdwS0pC4J0ls8S/WLB/HEt1K9XL841tTXtJ051LTvse3R1o7ba98a+9S6xTzjPgQiENDqKM1xhJUnxm4JaEldEqy16MrcpfrFg3hj9XL94lhqf1En9z16jzbbb1nv8d2jjcrNysyqk/xghEAkAlodpTmOtAOItTsCWlKXBOktniV67SCe+Fail2u1saa+pu3MoqZ9j22PtnbcXvvW2KfWabnGYxDonYBWR2mOe1914uuagJbUJQFbi67MXaLXDuKN0cu12lhiX9PJYx69R5vtt6z3+O7RRuVmZWbVSX4wQiASAa2O0hxH2gHE2h0BLalLgvQWzxK9dhBPfCvRy7XaWFNf03ZmUdO+x7ZHWztur31r7FPrtFzjMQj0TkCrozTHva868XVNQEvqkoCtRVfmXqdfdhCvVC/XLRvX2V+mk8c9eo82229Z7/Hdo43KzcrMqpP8YIRAJAJaHaU5jrQDiLU7AlpSlwTpLZ7r9MsO4olv6/Ry3bKxpr6m7cyjpn2PbY+2dtxe+9bYp9Ytyzceh0DPBLQ6SnPc84oTW9cEcuHMSZ3Hbfr9/PPP082bN9Nnn322VX5tEyN82a492+N6dP3Hj+AgcI0EaI6vESZTQWAbCGhJXeJXbgY8P6v0qw7iic1Verlm1VhTX9N2ZlLTvse2R1s7bq99a+xT61blHM9BoFcCWh3lleNeV5u4QhDQkrokcGvRlblX6VcdxCvRyzWrxlX2V+nkOY/eo832W9Z7fPdoo3KzMrPqJD8YIRCJgFZHaY4j7QBi7Y7AlaQ+/UV6vPtemu18mA5PXl+O9/RZ2t+Zp/ndg/RP/7aZV47XHcQTh7zFu6a+pu3M73rsv04vDj5I89l76e7BL9OZLIyMZ79MB3ffS7P5B+ngxbt95LHt0V5f3BLg+NHjv1U7tW48FRQQaJ/AlTqaUqI5bn9diSAwAS2pz14cpLvz2XkT/EK6Hml2Lppma9EV1Mv06w7irdPL8+vGZfbX6eR5j96jzfa3Ri97YqEBTml54+zx3aPdKm6yiUaM1tin1o0IiUsh0A0BrY7SHHezvAQSkYCW1FebG2l2vpf2j746x2QtusJY06/6RjzRyajp5bmSsaa+pu3M5jrta/+Q0h6TNfHY9mivO26JZ8zo8d+qnVo3hgfXQqAXAlodpTnuZXWJIyQBLanPQbx9VXA37f/tXtqZzdPO/rN0ekHJWnQFsqYvOYi3Si/PlYya/RKdXOPRe7TZ/nbp5R9OF2+veLtvLr+dAm6+dbOu+dQ6WWdGCEQioNVRmuNIO4BYuyOgJbUEKa8A5mvy+4zfvsViQw1ayUE88c1a9LdB37Lvmd8V/982xHvp4NP9tLPsfciaVhakYLxit0AzvKRlvdX3qXVD3tyGQBQCWh2lOY6y+sTZJQEtqd8F+qt0uPftNFt41Tg/by26MveivvQg3jK9PF46Ltov1cl1Hr1Hm+1vo37VP6SEmdf3bYx7GNu62x7/rdqpdesY8DwEeiSg1VGa4x5XmpjCENCS+k3w8t/lO2l3dyfNZu/eb5yftxZdAbuoLz2It0wvj5eOi/ZLdXKdR+/RZvvbqT9NR/t5n3w/PT7+WjBdGT2+e7Tby+0KIvUBa+xT61TneRACnRPQ6ijNceeLTnh9E9CSOkcsrwSev53i1ZuPcJvtPExHp28+vsJadIXmUD/mIJ6ml8fGjEP7Y3RyrUfv0Wb726mX5vgH6eDkG8F0ZfT47tFuL7criNQHrLFPrVOd50EIdE5Aq6M0x50vOuH1TUBL6nTxecbvmuGzdHr08NKhPGvRFZpD/ZiDeJpeHhszDu2P0cm1Hr1Hm+1vp57mWPbGstGzblbt1LplsfM4BHomoNVRmuOeV5zYGiTwVTra/16a7R6kkwLvryb1hX7hbRQpyeNvPpXg367x66PHHMSTkKxFfxv0Lfue+en+0xzL3lo26tyWXX35cat2at1lr7kHgRgErtZRvgQkxsoTZSMEXqXnj++m+WyWSprj/HaG3/iN30h5fPPzOp0cfnjpFeJLgcsryvMP0l/9079eemrsHSnaYw/iiR3Ry/2xY019TduZ02bsr2+O81r/zd/8zdilenv9Zvx+O/3aGzXtW21PrVsLkQsg0CEBmuMOF5WQ+iBwdvIsfbJ3O+UkPf9d88pxboj/6I/+KN24cSP9yZ/8yaBBLuNhLboyu+jHHsRb1Mv9saPYH6uT6z16jzbbb1GfG+Pf+Z3fSb/3e7+X/vqv/1owjhpbjHsYoMd/q3Zq3TBebkMgCgGa4ygrTZyNEfgmnRz8IM13H6ZPj3+RDnZvpFWvHEtj/Gd/9mfpH/7hH9Lt27dHN8jWoitgsz77cevWrfTy5Ut5uHi8DvvFxpQLPfY92uxKa3ppjP/yL//y7X6zNMitxb24bTz+W7VT6xZj5j4EIhCgOY6wysTYOIEvVjbHw8b4H//xH1P+tTTI1qIrcLPechBvqJfblvE6/LfYzZqatqe2P2yMF/fb2AY5ErfFvWWNfWrdot/ch0AEAjTHEVaZGBsnsLw51hrjxYYlv8Wi5MdadGXurLccxBvq5bZlvA7/LXazpqbtKe1rjfHifhvTIEfhpu0ra+xT6zTfeQwCvROgOe59hYmvAwLLm+P89oX8vs/839vSpAzH/DaL3/7t3z5v3nJR3eTv06dP082bNzdqY5P+M/f6/fH3f//36bd+67fS3/3d3y3db3/wB3/AHthwrln3agd/DAkBApMQoDmeBDNGIOAhsLw5zrMuezUvN8a/+7u/e/58ifVccD0/9+7dS0+ePDFP4bVfU1/TdgY+pf0f//jH5//gWmyQ837LB0Lz/2aU/kzpt+ZTTftW21PrNG48BoHeCdAc977CxNcBgdXNcQ5wsUEe2xjnOaxFN2tzQ5RfNbYcxJMF8tj3+u/Vt+y7JfbFBtnSGFvsZs3wp2XuVt+n1g15cxsCUQjQHEdZaeJsmMD65jgHJw3yH/7hH456xVjAWItu1ueDeHfu3JGpTKPHfjZYU1/Tdq3YpUH+4z/+49GvGMsGicjNG7uVmVUn/jJCIBIBmuNIq02sjRIoa45zcLlBzu8JzePYH0/xzAfxHj16NNbkpes99vNENfU1bdeMPTfI+VXjMW+lGC56VG6eNbMys+qG68VtCEQhQHMcZaWJMwwBLalLgrcWz9yI5882turFt5b1Lfue+Xv8r6X1+l1bb+U2tU7ykxECkQhodXS2CEC7aPEa7kMAAttBwJqv1qIr34hn1Qu1lvUt+575e/yvpfX6XVtv5Ta1TvKTEQKRCGh1lOY40g4g1u4IaEldEqSl6Ob/TpdvxLPoh361rG/Z97wGHv9rab1+19ZbuU2tG+YotyEQhYBWR2mOo6w+cXZJQEvqkkAtRXf4jXgW/dCvlvUt+57XwON/La3X79p6K7epdcMc5TYEohDQ6ijNcZTVJ84uCWhJXRKopegOvxHPoh/61bK+Zd/zGnj8r6X1+l1bb+U2tW6Yo9yGQBQCWh2lOY6y+sTZJQEtqUsCHVt05SCezD1WLzoZW9a37Hvm7/G/ltbrd229ldvUOslPRghEIqDVUZrjSDuAWLsjoCV1SZBji64cxJO5x+pFJ2PL+pZ9z/w9/tfSev2urbdym1on+ckIgUgEtDpKcxxpBxBrdwS0pC4JckzRHR7Ek7nH6EUzHFvWt+x7XgOP/7W0Xr9r663cptYNc5TbEIhCQKujNMdRVp84uySgJXVJoGOK7vAgnsw9Ri+a4diyvmXf8xp4/K+l9fpdW2/lNrVumKPchkAUAlodpTmOsvrE2SUBLalLAh1TdIcH8WTuMXrRDMeW9S37ntfA438trdfv2nort6l1wxzlNgSiENDqKM1xlNUnzu4I5MKZkzqPm/p9+vRpunnz5sbm35TfzLu5PQHbNth29wePgCCwIQI0xxsCy7QQqEVAS+oSX3KDU/KzeBBPNKV6uX5xbFnfsu95HTz+19J6/a6tt3KbWreYp9yHQAQCWh3lleMIK0+M3RLQkrok2JKiqx3Ek7lL9HKtNrasb9n3vBYe/2tpvX7X1lu5Ta3TcpXHINA7Aa2O0hz3vurE1zUBLalLAi4putpBPJm7RC/XamPL+pZ9z2vh8b+W1ut3bb2V29Q6LVd5DAK9E9DqKM1x76tOfF0T0JK6JOCSoqsdxJO5S/RyrTa2rG/Z97wWHv9rab1+19ZbuU2t03KVxyDQOwGtjtIc977qxNc1AS2pSwJeV3QXvxFvcc51+sXrF++3rG/Z97wOHv9rab1+19ZbuU2tW8xT7kMgAgGtjtIcR1h5YuyWgJbUJcGuK7rLDuLJ3Ov0ct2ysWV9y77n9fD4X0vr9bu23sptat2yfOVxCPRMQKujNMc9rzixdU9AS+qSoFcV3VUH8WTuVXq5ZtXYsr5l3/OaePyvpfX6XVtv5Ta1blXO8hwEeiWg1VGa415Xm7hCENCSuiTwVUV31UE8mXuVXq5ZNbasb9n3vCYe/2tpvX7X1lu5Ta1blbM8B4FeCWh1lOa419UmrhAEtKQuCXxV0V11EE/mXqWXa1aNLetb9j2vicf/Wlqv37X1Vm5T61blLM9BoFcCWh2lOe51tYkrBAEtqUsCX1Z01x3Ek7mX6eX5dWPL+pZ9z+vi8b+W1ut3bb2V29S6dXnL8xDokYBWR2mOe1xpYgpDQEvqkuCXFd11B/Fk7mV6eX7d2LK+Zd/zunj8r6X1+l1bb+U2tW5d3vI8BHokoNVRmuMeV5qYwhDQkrokeK3olhzEk7k1vTxXMrasb9n3vDYe/2tpvX7X1lu5Ta0ryV2ugUBvBLQ6SnPc2yoTTygCWlKXANCKbslBPJlb08tzJWPL+pZ9z2vj8b+W1ut3bb2V29S6ktzlGgj0RkCrozTHva0y8YQioCV1CQCt6JYcxJO5Nb08VzK2rG/Z97w2Hv9rab1+19ZbuU2tK8ldroFAbwS0Okpz3NsqE08oAlpSlwBYLLqlB/Fk7kW9PF46tqxv2fe8Ph7/a2m9ftfWW7lNrSvNX66DQE8EtDpKc9zTChNLKAK5cOakzqP39969e+nBgwfuebx+oPevJQxhmPcAPxCAQBkBmuMyTlwFgWYIaEld4vyweI45iCdzD/Xy2JixZX3Lvuc18vhfS+v1u7beym1q3Zgc5loI9EJAq6O8ctzL6hJHSAJaUpeAGBbdMQfxZO6hXh4bM7asb9n3vEYe/2tpvX7X1lu5Ta0bk8NcC4FeCGh1lOa4l9UljpAEtKQuATEsumMO4sncQ708NmZsWd+y73mNPP7X0nr9rq23cptaNyaHuRYCvRDQ6ijNcS+rSxwhCWhJXQJCiu7Yg3gyt+jl/tixZX3Lvud18vhfS+v1u7beym1q3dg85noI9EBAq6M0xz2sLDGEJaAldQkMKbql34i3OKfoFx8vvd+yvmXf8/p4/K+l9fpdW2/lNrWuNH+5DgI9EdDqKM1xTytMLOEIaEldAiEXXctBPJnbWrR70BO7rOK4EW7jeOWrrcysuvEeooBA+wS0Okpz3P66EkFgAlpSl+DIxdNyEE/m9hbflvUt+57Xz+N/La3X79p6K7epdZLfjBCIRECrozTHkXYAsXZHQEvqkiBz0bUcxJO5rUW7Bz2xyyqOG+E2jle+2srMqhvvIQoItE9Aq6M0x+2vKxEEJqAldQmOp0+fplu3bpVcql7jLb4t61v2PS+mx/9aWq/ftfVWblPr1GTnQQh0TkCrozTHnS864fVNQEvqkojzN+I9efKk5FL1GmvRlsla1rfse+bv8b+W1ut3bb2V29Q6yU9GCEQioNVRmuNIO4BYuyOgJfW6IPNBvJs3b6aXL1+uu3Tp89aiLRO2rG/Z98zf438trdfv2nort6l1kp+MEIhEQKujNMeRdgCxdkdAS+p1QeaDeHfu3Fl32crnrUVbJm1Z37Lvmb/H/1par9+19VZuU+skPxkhEImAVkdpjiPtAGLtjoCW1OuCzAfxHj16tO6ylc9bi7ZM2rK+Zd8zf4//tbRev2vrrdym1kl+MkIgEgGtjtIcR9oBxNodAS2pVwUp34hnLboyd2Q9scsuGDfCbRyvfLWVmVU33kMUEGifgFZHaY7bX1ciCEogF8Cc1Hks/c0H8R48eFB8fem8XFe+BrCC1RR7IOifRcKGwGgCNMejkSGAwHYT0JJ6mcfDb8TLxdnzE1lP7LadA7fx3KzMrLrxHqKAQPsEtDrKK8ftrysRBCagJfUyHMNvxPMWz8h6Yl+2w1Y/DrfVfLRnrcysOs0HHoNA7wS0Okpz3PuqE1/XBLSkXhbw8BvxvMUzsp7Yl+2w1Y/DbTUf7VkrM6tO84HHINA7Aa2O0hz3vurE1zUBLam1gOUgnjznLZ6R9cQuu2jcCLdxvPLVVmZW3XgPUUCgfQJaHaU5bn9diSAwAS2pNRwfffTRpW/E8xbPyHpi13bY+sfgtp7R4hVWZlbdon3uQyACAa2O0hxHWHli7JaAltSLwQ4P4slz3uIZWU/ssovGjXAbxytfbWVm1Y33EAUE2ieg1VGa4/bXlQgCE9CSehHH8CCePOctnpH1xC67aNwIt3G88tVWZlbdeA9RQKB9AlodpTluf12JIDABLakXcQwP4slz3uIZWU/ssovGjXAbxytfbWVm1Y33EAUE2ieg1VGa4/bXlQgCE9CSeohj8SCePOctnpH1xC67aNwIt3G88tVWZlbdeA9RQKB9AlodpTluf12JIDABLamHOBYP4slz3uIZWU/ssovGjXAbxytfbWVm1Y33EAUE2ieg1VGa4/bXlQgCE9CSWnBoB/HkOW/xjKwndtlF40a4jeOVr7Yys+rGe4gCAu0T0OoozXH760oEgQloSS04tIN48py3eEbWE7vsonEj3MbxyldbmVl14z1EAYH2CWh1lOa4/XUlgsAEtKQWHNpBPHnOWzwj64lddtG4EW7jeOWrrcysuvEeooBA+wS0Okpz3P66EkFgAlpSZxzLDuIJKm/xjKwndtlF40a4jeOVr7Yys+rGe4gCAu0T0OoozXH760oEgQloSZ1xLDuIJ6i8xTOynthlF40b4TaOV77aysyqG+8hCgi0T0CrozTH7a8rEQQlkAtgTuo8Dn8///zzdPPmzfTZZ59denx4DbcvM4MHPHrbA0H/LBI2BEYToDkejQwBBLabgJbUqw7iSTS5EfD8RNYTu23nwG08Nyszq268hygg0D4BrY7yynH760oEgQloSb3qIJ6g8hbPyHpil100boTbOF75aiszq268hygg0D4BrY7SHLe/rkQQmMBiUq87iCeovMUzsp7YZReNG+E2jle+2srMqhvvIQoItE9gsY7miGiO219XIghMYDGp1x3EE1Te4hlZT+yyi8aNcBvHK19tZWbVjfcQBQTaJ7BYR3NENMftrysRBCYwTOpV34i3iMhbPCPriX1xN5Xdh1sZp+FVVmZW3dA2tyEQhcCwjkrMNMdCghECDRIYJnXJQTwJ0Vs8I+uJXXbRuBFu43jlq63MrLrxHqKAQPsEhnVUoqE5FhKMEGiQwDCpSw7iSYje4hlZT+yyi8aNcBvHK19tZWbVjfcQBQTaJzCsoxINzbGQYIRAgwQkqUsP4kmI3uIZWU/ssovGjXAbxytfbWVm1Y33EAUE2icgdXQYCc3xkAa3IdAYAUnq0oN4Ep63eEbWE7vsonEj3MbxyldbmVl14z1EAYH2CUgdHUZCczykwW0INEYgJ/WYg3gSnrd4RtYTu+yicSPcxvHKV1uZWXXjPUQBgfYJ0By3v4ZEAIFLBHJSjzmIJ2Jv8YysJ3bZReNGuI3jla+2Mhvqjo+PxxtGAYFABGiOAy02ocYgkJN6zEE8oTIsnvLYmDGyntjH7JR318LtHYvSW1ZmQ93777+f8m/+RzQ/EIDAVQI0x1eZ8AgEmiaQk/rWrVujYxgWz9FixytaYqtl+y37nvl7/K+l9fpdW2/ldl263BjTJMtfH0YIXCZAc3yZB/cg0DyBnNRPnjwZHYe16IqhyHpil10wboTbOF75aiuzZTqa5PFrgKJ/AjTH/a8xEQYjkJP65cuXo6NeVjxLJ4qsJ/bSXXL5Orhd5lFyz8psnW7YJP/85z8vcYVrINAtAZrjbpeWwLaZQE48fmHAHmAPbOse2Oa/n/gGgU0TyHm5+HPlEe2iRRH3IQCB7SBAvm7HOuAFBFogkP+XKX8mej6ncHBwcP4xkC34jY8Q2CQBrY7SHG+SOHNDYMMEtKTesEmmhwAEGiNAU9zYguHupAS0OkpzPOkSYAwC10tAS+rrtcBsEIBAywR4pbjl1cP3KQhodZTmeAry2IDAhghoSb0hU0wLAQg0SCAfvsvfoskPBCCgE9DqKM2xzopHIdAEAS2pm3C8ppOnz9L+zntp9+CLml60YfvsJB19spd23h4qHMFKyQAACC5JREFUvZ32PnmWTs7acL+el6/S8cH9d9zmu2n/0+N0Ws8hLEMAAksIaHWU5ngJLB6GQAsEtKRuwe9qPp7+Ij3efS/NZjdojtcuwlfpaP97aTbfTQ+fnaSzdJZOn3+SdufztLP/jEZvKb/X6cXBB2k+u53uH75IZ+l1Ojn8MO3M3kt3D36Z+HfFUnA8AYEqBLQ6SnNcZSkwCoHrIaAl9fXM3Nssr9PJ0f9Oezvzi4/Vozleu8LfHKX9G7M03ztMr95efJqO9nfSbH4/Hb6izXuLZXjj7Hl6fHt+mdsFyxv7R+mb4bXchgAEqhPQ6ijNcfVlwQEI2AloSW2frWflF+lg9ztpd/+f0/Hx/0m7vHK8frFPj9PhwUH60VF+1Vh+fpUO975Ncyw4Ssa3b02Z6pXjs/Tq8H6a7x6kk0X/Tg7Y+4tMuB+egFZHaY7DbwsAtExAS+qW45nEdxoEM+azFwfp7nyW5ncP0ot3HbN5vr6F36STgx+8/QKg6Zjlf8B8J91+/Hzwj5oL0uz9vrcc0ZkIaHWU5tiEEhEEtoOAltTb4dkWe0GDYFqcs5NP0/38tpT53fT4+bs3WpgmCyV6nU6efZx28z8qLr1FZUMQXh2mvfn30+Pjr68aYO9fZcIj4QlodZTmOPy2AEDLBLSkbjmeSXynQRiJ+SydHh+8eb82jfFIdnL5xdtRZj9IByebfdfxN0f76cbtx+lYe2V/Ye/LP3jmu5+k56ev37zSnT9Z42/ffULJfPfj9NOjw/Tw/CBr/grw22nv4DkHMmVpGZsnoNVRmuPml5UAIhPQkjoyj6LYFxqEIk3Yi+QTKma8YuzaA/IWi7HNcX6v/I00m83fvE3i7CQ9e7ib5rNvp73DXykefZ2OH39/+SvUg71/uTHOnbT4OE87ewfp+PSbi08nedMQv/nkjYtPMJkteWVa8YiHILDtBLQ6SnO87auGfxBYQUBL6hWX81QmMGgQALKKwKAx3rmfDo55K8UqWm+fO39bw0Uz+/ZBz0HGi4+Gu/3f0+P9D1e/peX8kzK+s6Rxfrf3/8v+x+n+zo20c//TwWdWS3M8aHwvPnljNjjcd/7K9Gwn7R/xqc1vl5cbTRPQ6ijNcdNLivPRCWhJHZ3J2vhpjtciOr/g/MtS8nuMP0gHL16XabgqpSSfDy3vzZYvBHF8WsV5w71ef3b8ON1e9TF753s/vxKcfxc/r1qa4+Gr229euR5+BB3NMZu8NwJaHaU57m2ViScUAS2pQwGwBEtzXETtTRMkjdTiOGygiqaLddHbj2+74Ob+hrzcpL6nfwLFW7IrPsJNrjnf+/O0c/9H6fBvv59ms++l/aOvLp6lORZMjLEIaHWU5jjWHiDazghoSd1ZiIQDgeAEztLp0cdpd+fby99LfE5oxUe4CcHhPwzlfwZ2Hqaj0+F7jof/8OGVY0HH2C8BrY7SHPe73kQWgICW1AHCJkQIhCGQD879t/s/Sl88v3jLxFcv0r//+/CLWS5QrPoIN6E1bI7z14EfPRx8rTWvHAsmxlgEtDpKcxxrDxBtZwS0pO4sRMKBQFACF59UsfNhOjx5nZJ8LfXux+lZvr/ws/Ij3OTaS81xflDeH53fV/4fF19awivHgosxBgGtjtIcx1h7ouyUgJbUnYZKWBCAAAQgAIFrJ6DVUZrja8fMhBCYjoCW1NNZxxIEIAABCECgbQJaHaU5bntN8T44AS2pgyMhfAhAAAIQgEAxAa2O0hwX4+NCCGwfAS2pt89LPIIABCAAAQhsJwGtjtIcb+da4RUEighoSV0k5CIIQAACEIAABM6/FGcRA83xIhHuQ6AhAjTHDS0WrkIAAhCAwNYR0OoozfHWLRMOQQACEIAABCAAAQhMQYDmeArK2IAABCAAAQhAAAIQaIIAzXETy4STEIAABCAAAQhAAAJTEKA5noIyNiAAAQhAAAIQgAAEmiBAc9zEMuEkBCAAAQhAAAIQgMAUBGiOp6CMDQhAAAIQgAAEIACBJgjQHDexTDgJAQhAAAIQgAAEIDAFAZrjKShjAwIQgAAEIAABCECgCQI0x00sE05CAAIQgAAEIAABCExBgOZ4CsrYgAAEIAABCEAAAhBoggDNcRPLhJMQgAAEIAABCEAAAlMQoDmegjI2IAABCEAAAhCAAASaIEBz3MQy4SQEIAABCEAAAhCAwBQEaI6noIwNCEAAAhCAAAQgAIEmCNAcN7FMOAkBCEAAAhCAAAQgMAUBmuMpKGMDAhCAAAQgAAEIQKAJAjTHTSwTTkIAAhCAAAQgAAEITEGA5ngKytiAAAQgAAEIQAACEGiCAM1xE8uEkxCAAAQgAAEIQAACUxCgOZ6CMjYgAAEIQAACEIAABJogQHPcxDLhJAQgAAEIQAACEIDAFARojqegjA0IQAACEIAABCAAgSYI0Bw3sUw4CQEIQAACEIAABCAwBQGa4ykoYwMCEIAABCAAAQhAoAkCNMdNLBNOQgACEIAABCAAAQhMQYDmeArK2IAABCAAAQhAAAIQaIIAzXETy4STEIAABCAAAQhAAAJTEKA5noIyNiAAAQhAAAIQgAAEmiBAc9zEMuEkBCAAAQhAAAIQgMAUBGiOp6CMDQhAAAIQgAAEIACBJggUN8f5Qn5hwB5gD7AH2APsAfYAe4A90PseWOziZ4sPcB8CEIAABCAAAQhAAAJRCdAcR1154oYABCAAAQhAAAIQuEKA5vgKEh6AAAQgAAEIQAACEIhKgOY46soTNwQgAAEIQAACEIDAFQI0x1eQ8AAEIAABCEAAAhCAQFQC/x+qOOEd3vON7AAAAABJRU5ErkJggg=="></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, for observer A, the length<em> L</em><sub>A</sub> of the bridge</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, for observer A, the time taken to cross the bridge.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Outline why<em> L</em><sub>B</sub> is the proper length of the bridge.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>'</em>.</span></p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Demonstrate using the diagram which lamp, according to observer A, was <strong>turned on</strong> first.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Demonstrate, using the diagram, which lamp observer A <strong>observes</strong> to light first.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Determine the time, according to observer A, between X and Y.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(iv).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Two protons are moving to the right with the same speed <em>v</em> with respect to an observer at rest in the laboratory frame.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Outline why there is an attractive magnetic force on each proton in the laboratory frame. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain why there is no magnetic force on each proton in its own rest frame.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain why there must be a resultant repulsive force on the protons in all reference frames.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates of special relativity.</p>
</div>
<br><hr><br>