Concepts of Physics
Concepts of Physics PHYS 100
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Date Created: 11/01/15
Phys 100 Spring 2009 Concepts of Physics Class Exercise 4 Money and energy analogy Two people are stranded on a deserted and isolated island Alice carries 50000 in United States dollars and Zach carries R500000 South African Rand The Rand is the currency of South Africa and currently one US dollar is worth ten Rand a Determine the total amount of money on the island in US dollars b Would you say that Alice s money is all in one form or in more than one form What about Zach s money and all of the money on the island c Suppose that Alice exchanges 20000 of her money with Zach at the rate given above How much does she hold in US dollars and how much in South African Rand How much money does Alice have in total Did this change during the exchange d After the exchange7 how much does Zach hold in each currency How much money does Zach have in total Did this change during the exchange e After a series of such exchanges7 does the total amount of money that Alice holds change What about Zach f Is the total amount of money held by Alice conserved assuming that all transactions are fair 2 Skater and a Ramp A skater of mass 100 kg is initially at rest at the top of a ramp At this point the skater is 10m above the ground The skater then slides down the ramp Instant Kinetic Energy Potential Energy Total Energy Initial Moment 5 m above ground At ground a Determine the potential7 kinetic and total energy of the skater at this initial moment and enter these into the table b What can one say about the value of the total energy throughout the motion O V Determine the potential7 kinetic and total energy of the skater at the moment when he is 5 m above the ground and enter these into the table CL V Determine the potential7 kinetic and total energy of the skater at the moment when he is at the ground and enter these into the table D Determine the speed of the skater at all three moments 3 Stopped pendulum A pendulum is released from rest at the illustrated position The string encounters a peg in its path Which indicates the highest point that the pendulum ball reaches after the string strikes the peg Release Highest point 9 4 o 3 2 1 i Phys 100 Spring 2009 Concepts of Physics Class Exercise 7 Particle diffraction and uncertainties in position and velocity Consider a particle initially moving vertically and passing through a single slit as shown in Fig 1 The probability of the particle arriving at various locations on the detection screen is illustrated in Fig 1 The horizontal axis indicates the initial horizontal position of the particle when it is red Probability of particle arrival 4 A Screen w B A Slit and barrier Particle i i lnitial horizontal position Figure 1 Particle diffraction by a single slit a The barrier and slit can be shifted horizontally so that the slit only picks out particles that were red from one particular location Consider the situation illustrated below7 in which the particle could have been red from one of several locations Slit and barrier T Particles 73 72 fl 0 l 2 3 4 lnitial horizontal position If the particle does appear on the screen beyond the slits7 indicate the location from which it was red With reference to the axis7 what was the value of its initial horizontal position Give at least two values which do not accurately describe its initial horizontal position b In the previous case7 what was the horizontal position of the particle immediately after it passed through the slitf2 c Now suppose that the slit is shifted to the right as illustrated Slit and barrier T Particles 74 73 72 71 0 1 2 3 4 l l l l l l l l 1 Initial horizontal position With reference to the axis7 what was the value ofthe particle s initial horizontal position Give at least two values which do not accurately describe its initial horizontal position What was the horizontal position of the particle immediately after it passed through the slit in this case d The previous examples show that the slit can be used to measure the particle s horizontal position immediately before and after passing through the slit Now suppose that the slit is widened as illustrated Slit and barrier T Particles 74 73 72 71 0 l 2 3 4 l l 1 Initial horizontal position With reference to the axis7 what was the value ofthe particle s initial horizontal position What was the horizontal position of the particle immediately after it passed through the slit in this case e As the slit is widened what happens to the precision with which its position is known V h V an 3 V immediately after passing through the slit Does the precision increase decrease or stay the same Suppose that the particle arrives at the location labeled A in Fig 1 To do so it must have traveled directly from the slit to the screen Sketch its trajectory the route that it takes Thus immediately after passing through the slit it must have both a vertical and a horizontal component of velocity How does the horizontal component of velocity immediately after passing through the slit of a particle which arrives at A compare to that which arrives at B Is it the same smaller or larger As the width of the central probability peak w increases what does this imply for the range of values possible for the horizontal component of velocity immediately after passing through the slit It is found experimentally that 7 2L w 7 a where hmv is the wavelength of the particle immediately before passing through the slit L is the distance from the slit to the screen and a is the width of the slit Suppose that the slit is widened while everything else is held xed How does this affect the precision with which the horizontal component of velocity immediately after passing through the slit is known Does the precision increase decrease or stay the same Fill out the following table indicating what happens to the precision with which the horizontal position and velocity are known immediately after the particle passes through the slit Action Horizontal position precision Horizontal velocity precision Slit widens Slit narrows j ls it possible to arrange for the slit to be such that the particle s position and velocity are both known precisely immediately after passing through the slit This is an example of the Heisenberg uncertainty principle which limits the precision with which both the position and velocity of a particle can be known with certainty The actual uncertainty principle states that if the typical spread in values of the position is Am and the typical spread in velocity is Av then the product Am x Av must be greater than h47rm where m is the mass of the particle Experiments7 in which particles are red through single slits as described in this exercise verify that the uncertainty principle is valid PMS 00 Sym 04 ch rwe 3 Ammw me m ths 7ch Emma Mm My we WA 43min ml be WM 7 wag a objed39s and 11 1amp2 bun ldx j blocks all aged As an M0109 m MSW cami452 a pmmka Wlm l does Vacs awn 1 is mach a 9mm MMme Q30 w O 233 Georg amp 39Pmcaka is ad some sor r a bank Wa 3040 HM we WW6 basic 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