Problem Set 7 & Solutions

Problem Set 7 & Solutions - m during the time interval...

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Phys116 Problem Set 7 Due: Friday, Oct. 24, 2003 before the start of class. Please write your TA’s name at the top of your solution set. Communicate your reasoning in your solutions, concisely and clearly. Efforts are as important as correct answers. 1. K&K, problem 4.2. 2. K&K, problem 4.6. 3. K&K, problem 4.10. 4. K&K, problem 4.14. 5. K&K, problem 4.24. 6. K&K, problem 2.34 revisited: You solved this problem on a previous problem set, and found that the force on the string is F ( t ) = m w 0 r 0 4 r 0 - Vt ( ) 3 and the angular velocity w ( t ) of mass m as a function of time is w ( t ) = w 0 r 0 r 0 - Vt 2 . Since the string is pulled with constant velocity V , we can say that the displacement of the string is x = Vt , so that as a function of this distance the force on the string is F ( x ) = m w 0 r 0 4 r 0 - x ( ) 3 . (a) Calculate the work done by the force F(x) over some distance X = V T . Then using the expression for w ( t ), calculate the change in kinetic energy of the mass
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Unformatted text preview: m during the time interval that the force is applied. Should the work be equal to the change in kinetic energy? If it is not, name a non-conservative force in the problem. (b) Does this result seem strange to you? The force acts on the mass in the radial direction, basically perpendicular to the motion of the mass around the central ring. Explain, in terms of line integral of the forces acting on the mass, why there is any non-zero amount of work done on the mass to change its kinetic energy. (c) Explain why it is not a violation of the work-energy theorem that it is the velocity in the ˆ q direction that changes, even though the force is entirely in the ˆ r direction. 7. K&K, problem 4.20. Are there any non-conservative forces acting in this problem?...
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