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Chapter 9: Q14 P (page 377)
A group of particles of total mass has a total kinetic energy of . The kinetic energy relative to the center of mass is . What is the speed of the center of mass?
The speed of the center of mass is
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A box contains machinery that can rotate. The total mass of the box plus the machinery is. A string wound around the machinery comes out through a small hole in the top of the box. Initially the box sits on the ground, and the machinery inside is not rotating (left side of Figure 9.61). Then you pull upward on the string with a force of constant magnitude . At an instant when you have pulled 0.6mof string out of the box (indicated on the right side of Figure 9.61), the box has risen a distance of 0.2 mand the machinery inside is rotating.
POINT PARTICLE SYSTEM (a) List all the forms of energy that change for the point particle system during this process. (b) What is thecomponent of the displacement of the point particle system during this process? (c) What is the ycomponent of the net force acting on the point particle system during this process? (d) What is the distance through which the net force acts on the point particle system? (e) How much work is done on the point particle system during this process? (f) What is the speed of the box at the instant shown in the right side of Figure 9.61? (g) Why is it not possible to find the rotational kinetic energy of the machinery inside the box by considering only the point particle system?
EXTENDED SYSTEM (h) the extended system consists of the box, the machinery inside the box, and the string. List all the forms of energy that change for the extended system during this process. (i) What is the translational kinetic energy of the extended system, at the instant shown in the right side of Figure 9.61? (j) What is the distance through which the gravitational force acts on the extended system? (k) How much work is done on the system by the gravitational force? (I) what is the distance through which your hand moves? (m) How much work do you do on the extended system? (n) At the instant shown in the right side of Figure 9.61, what is the total kinetic energy of the extended system? (o) what is the rotational kinetic energy of the machinery inside the box?
Consider the voyage to the Moon that you studied in Chapter 3. Would it make any difference, even a very tiny difference, whether the spacecraft is long or short, if the mass is the same? Explain briefly.
Tarzan, whose mass is 100kg, is hanging at rest from a tree limb. Then he lets go and falls to the ground. Just before he lets go, his center of mass is at a height 2.9m above the ground and the bottom of his dangling feet are at a height 2.1 above the ground. When he first hits the ground he has dropped a distance 2.1, so his center of mass is (2.9-2.1) above the ground. Then his knees bend and he ends up at rest in a crouched position with his center of mass a height above the ground. (a) Consider the point particle system. What is the speed v at the instant just before Tarzan's feet touch the ground? (b) Consider the extended system. What is the net change in internal energy for Tarzan from just before his feet touch the ground to when he is in the crouched position?
A box and its contents have a total mass. A string passes through a hole in the box (Figure), and you pull on the string with a constant force(this is in outer space—there are no other forces acting).
(a) Initially the speed of the box was. After the box had moved a long distance, your hand had moved an additional distance(a total distance of), because additional string of lengthcame out of the box. What is now the speedof the box? (b) If we could have looked inside the box, we would have seen that the string was wound around a hub that turns on an axle with negligible friction, as shown in Figure. Three masses, each of mass, are attached to the hub at a distancefrom the axle. Initially the angular speed relative to the axle was. In terms of the given quantities, what is the final angular speed relative to the axis,?
A sphere or cylinder of mass M, radius R and moment of inertia I rolls without slipping down a hill of height h, starting from rest. As explained in problem P.33, if there is no slipping . (a) In terms of given variables (M,R,I and h), what is at the bottom of hill? (b) If the object is a thin hollow cylinder, what is at the bottom of hill? (c) If the object is a uniform density hollow cylinder, ), what is at the bottom of hill? (d) If the object is a uniform density sphere what is at the bottom of hill? An interesting experiment that you can perform that is to roll various objects down an inclined board and see how much time each one takes to reach the bottom.
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