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ps07_solns - Physics 1111 Fall 2008 PS#7 Solutions Page 1...

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Physics 1111 Fall 2008 PS #7 Solutions Page 1 of 5 Physics 1111 Problem Set #7 Solutions Problem 1: Choose whether each of the following statements is true or false. (a) You drop a ball to the ground from rest, and, from the same height, throw a second ball down to the ground. Their change in gravitational potential energies are different. (b) If the potential energy of the system is zero, the force on the object is zero. (c) If the force on an object is zero, the potential energy of the system is zero. (d) The potential energy of a system can be negative. (e) When air resistance is taken into account, a ball thrown directly upward spends more time on the way down than on the way up. (a) False. The potential energies of the balls do not depend on their velocities, only their positions. Since they begin and end in the same place, their changes in potential energy are identical. (b) False. If I drop a ball, but take the my potential energy “reference height” to be the initial height of the ball, then its initial potential energy is zero even though there’s a force on it. (c) False. If there are no forces acting on an object (i.e., not just no net force, but none at all), one can say that its potential energy is constant. However, that constant value can be arbitrary, because only differences in potential energy matter. The constant needn’t be zero. (d) True. The “reference height” can be at any location, in which case everything below that height will have a negative gravitational potential energy. (e) True. This is the most challenging of the true/false statements. One way to answer it is to realize that the ball’s final speed when it reaches you again will be less than its initial speed, because air resistance has done non-conservative work on the ball and has reduced its kinetic energy. This means that the ball had a higher average speed on the way up than on the way down. Since the ball traveled the same distance up and down, it must have taken longer on the way down. Another way to think about this problem, without using energy, is to look at the forces acting on the ball. On the way up, gravity and air resistance are both acting downward on the ball. As the ball falls, however, gravity pulls down while air resistance opposes it. Since tha ball has a greater net force acting on it on the way up, it will slow down more quickly.
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Physics 1111 Fall 2008 PS #7 Solutions Page 2 of 5 Problem 2: Two objects of unequal mass are connected by a massless rope that passes over a massless, frictionless pulley. After the objects are released from rest, what can be said about the
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