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Chapter 9: Q43_P (page 381)

A string is wrapped around a uniform disk of mass M and radius R. Attached to the disk are four low-mass rods of radius b, each with a small mass m at the end (Figure 9.63).

The apparatus is initially at rest on a nearly frictionless surface. Then you pull the string with a constant force F. At the instant when the center of the disk has moved a distance d, an additional length w of string has unwound off the disk. (a) At this instant, what is the speed of the center of the apparatus? Explain your approach. (b) At this instant, what is the angular speed of the apparatus? Explain your approach.

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Most popular questions from this chapter

A uniform-density sphere whose mass is 10kgand radius is 0.4mmakes one complete rotation every0.2s. What is the rotational kinetic energy of the sphere?

Two identical 0.4 kgblock (labeled 1 and 2) are initially at rest on a nearly frictionless surface, connected by an unstretched spring, as shown in the upper portion of Figure 9.59.

Then a constant force of 100 N to the right is applied to block 2 and at a later time the blocks are in the new positions shown in the lower portion of Figure 9.59.9.59. At this final time, the system is moving to the right and also vibrating, and the spring is stretched. (a) The following questions apply to the system modeled as a point particle. (i) What is the initial location of the point particle? (ii) How far does the point particle move? (iii) How much work was done on the particle? (iv) What is the change in translational kinetic energy of this system? (b) The following questions apply to the system modeled as an extended object. (1) How much work is done on the right-hand block? (2) How much work is done on the left-hand block? (3) What is the change of the total energy of this system? (c) Combine the results of both models to answer the following questions. (1) Assuming that the object does not get hot, what is the final value of Kvib+Uspringfor the extended system? (2) If the spring stiffness is 50 N/m, what is the final value of the vibrational kinetic energy?

A man whose mass is 80kg and a woman whose mass is 50kgsit at opposite ends of a canoe 5m long, whose mass is 30kg. (a) Relative to the man, where is the mass of the system consisting of man-woman, and canoe? (Hint: Choose a specific coordinate system with a specific origin.) (b) Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water? Explain your work and your assumptions.

Consider a system consisting of three particles:

m1=2kg,v鈫�1=(8,-6,15)m/sm2=6kg,v鈫�2=(-12,9,-6)m/sm3=4kg,v鈫�3=(-24,34,23)m/s

What isKrel, the kinetic energy of this system relative to the centre of mass?

Question: Under what conditions does the energy equation for the point particle system differ from the energy equation for the extended system? Give two examples of such a situation. Give one example of a situation where the two equations look exactly alike.
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