An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter A.1, Problem 4P
To determine
To Show: The energy of particle which travels at the
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(a) What is the momentum of a proton moving at 0.900c ? (b) At what speed will a particle’s relativistic momentum equal twice its classical momentum?
(a) Calculate the classical momentum of a proton traveling at 0.974c, neglecting relativistic effects. (Use 1.67 x 10-2 for the mass of the proton.)
4.87E35
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. kg · m/s
(b) Repeat the calculation while including relativistic effects.
2.15e36
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. kg • m/s
(c) Does it make sense to neglect relativity at such speeds?
O yes
no
(a) Prepare a graph of the relativistic kinetic energy and the classical kinetic energy, both as a function of speed, for an object with a mass of your choice. (b) At what speed does the classical kinetic energy underestimate the experimental value by 1%? (c) By 5%? (d) By 50%?
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An Introduction to Thermal Physics
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- One cosmic ray neuron has a velocity of 0.250c relative to the Earth. (a) What is the neutron's total energy in MeV? (b) Find its momentum. (c) Is in this situation? Discuss in terms of the equation given in part (a) of the previous problem.arrow_forwardShow that (x,t)=Asin(kxt) and (x,t)=Acos(kxt) do not obey Schrödinger's time-dependent equation.arrow_forwardIn the Check Your Learning section of Example 27.1, the author commented that even at z=0.2 , there is already an 11% deviation between the relativistic and the classical solution. What is the percentage difference between the classical and relativistic results at z=0.1 ? What is it for z=0.5 ? What is it for z=1 ?arrow_forward
- Check Your Understanding a. A particle travels at 1.90108m/sand lives 2.10108swhen at rest relative to an observer. How long does the particle live as viewed in the laboratory? b. Space craft A and B pass in opposite directions at a relative speed of 4.00107m/s . An internal clock in space craft A causes it to emit a radio signal for 1.00 s. The computer in spacecraft B corrects for the beginning and end of the signal having traveled different distances, to calculate the time interval during which ship A was emitting the signal. What is the time interval that the computer in spacecraft B calculates?arrow_forward(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.arrow_forwardThe mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.arrow_forward
- Suppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forwardPlans for ail accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity =11v2/c2be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?arrow_forwardThe kinetic energy of motion, 7, of a particle is the relativistic total energy minus the rest energy, i.e.. T=ymor²- moe², where is the speed of light. (a) A particle has rest mass mo and speed v. Ifc, then show that the kinetic energy due to motion is approximated by the well-known classical expression for the kinetic energy, i.e.. (b) What is the particle's speed if its kinetic energy 7 is equal to its rest energy? (c) Express the momentum p of the particle as a function of the rest mass mo and the kinetic energy of the motion, 7, Your expression should contain mo and T, not or [Hint: Use the relation between E and p that does not involveu ory.]arrow_forward
- (a) Calculate the classical momentum of a neutron traveling at 0.987c, neglecting relativistic effects. (Use 1.67 x 10-27 for the mass of the neutron.) kg. m/s (b) Repeat the calculation while including relativistic effects. kg • m/sarrow_forward(Low velocity limit of relativistic kinetic energy.) Starting from the relativistic expression for the kinetic energy of a particle, show that when the particle’s velocity is small compared to c, the kinetic energy is approximately equal to the classical value. Hint: you’ll need to use the binomial approximation.arrow_forward(a). What are the energies and energy eigenfunctions for a non-relativistic particle of mass m moving on a ring of radius R as shown in Fig. (a)? (b). What are the energies and eigenfunctions if the ring is doubled (each loop still has radius R) shown in Fig. (b)? (c) If the particle has a charge q. What are the energies and energy eigenfunctions if a very long solenoid containing a magnetic flux passes the rings, as shown in Fig. (c)? Assume the system does not radiate electromagnetically. Fig. (a) Fig. (b) Fig. (c)arrow_forward
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