Homework 9

Never enter units in your answers. Be sure to use the units indicated on the HW submission page. Enter numbers without commas. 23,546 should be 23546 Always enter a * for multiplication. g(H+h) should be g*(H+h).



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Submitted Answers will be graded W 11/12, Th 11/13, F 11/14, and M 11/17 at 12:00 noon.




Problem 9.1
	What you should learn: In this assignment and in the assignments that follow, reading the course material is very important.
	Problem: Did you read Chapter 39 Sections 1:3? Type Y or N in the box (for yes or no, obviously).
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Problem 9.2
	What you should learn: HW9 only covers the first sections of Chapter 39. In addition to the reading, I want you to be familiar with the material from the lecture.
	Problem: I would like you to review the Power Point Slides for Class 29. Did you review these slides? Type Y or N in the box.
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Problem 9.3
	What you should learn: The energy or "total energy" in relativity is given by the expression E = mγc2 and p = meffv where m is the rest mass. We will consistently use this notation for masses in the homework.
	Problem: For a particle moving at half the speed of light, which of the following are correct expressions for total energy? Express your answer as the sum of all correct responses. For example, if only A and B were correct, your answer should be A+B. A. E = mc2 B. E = meffc2 C. E = pc D. E = E0γ  where E0 is the rest energy.
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Problem 9.4
	What you should learn: The energy or "total energy" in relativity is given by the expression E = mγc2 and p = meffv where m is the rest mass. We will consistently use this notation for masses in the homework.
	Problem: For a particle at rest, which of the following are correct expressions for total energy? Express your answer as the sum of all correct responses. For example, if only A and B were correct, your answer should be A+B. A. E = mc2 B. E = meffc2 C. E = pc D. E = E0γ  where E0 is the rest energy.
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Problem 9.5
	What you should learn: The energy or "total energy" in relativity is given by the expression E = mγc2 and p = meffv where m is the rest mass. We will consistently use this notation for masses in the homework.
	Problem: For a moving particle, which of the following are correct expressions for pc? Express your answer as the sum of all correct responses. For example, if only A and B were correct, your answer should be A+B. A. pc = mγvc B. pc = meffγc2 C. pc = Ev/c D. pc = E0γv/c  where E0 is the rest energy.
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Problem 9.6
	What you should learn: In class we discussed the fact that relativistic mechanics and Newtonian mechanics have much in common mathematically when we view Newtonian mechanics from a "relativistic viewpoint."
	Problem: Which of the following statements is true? Express your answer as the sum of all correct responses. For example, if only A and B were correct, your answer should be A+B. A. We can consider time as a fourth dimension in Newtonian mechanics as well as in relativistic mechanics. B.  Both in Newtonian mechanics and relativistic mechanics E is what carries a particle to a new time just as pc carries a particle to a new position. C.  Both in Newtonian mechanics and relativistic mechanics c must be the speed of light. D. In Newtonian mechanics, time steps (for a fixed value of Δu) are always the same because E never changes. E. In relativistic mechanics, time steps (for a fixed value of Δu) are longer when velocity increases because E increases when kinetic energy increases.
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Problem 9.7
	What you should learn: In relativity we define force as did Newton: F = dp/dt. But is F=ma?
	Problem: We know that p = mγv where γ is a function of velocity we will know for the next homework assignment. Since acceleration is defined to be a = dv/dt, we wish to find an expression that relates force to acceleration. A. F = ma B. F = mγa C. F = ma + mv dγ/dt D. F = mγa + mv dγ/dt E. F cannot be determined until we know γ.
	Hints: All you need is the product rule and the expressions for force and momentum.
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