Chapter 8: Potential Energy and Conservative Forces
Selected Solutions


Selected Solutions

1. Path #1 has 5 segments, the work done by each is calculated as W1 = -mg(Dy1 + Dy2 + Dy3 + Dy4 + Dy5).

W1 = -(2.6 kg)(9.81 m/s2)[4.0 m + 0 - 1.0 m + 0 - 1.0 m] = 51 J

Path #2 has 3 segments:

W2 = -(2.6)(9.81 m/s2)[0 + 2.0 m + 0] = -51 J

Path #2 has 3 segments:

W3 = -(2.6)(9.81 m/s2)[-1.0 m + 0 + 3.0 m] = -51 J

7. The potential energy of the spring is given by and we seek the compression . We can determine k from the given information


Given k, we can now calculate y,

15. The gravitational potential energy can be calculated for the different heights using U = mgy taking the ground as the reference. The kinetic energy at each height can be determined by using the fact that DK = -DU. Finally, the total mechanical energy E = K + U. The following table contains the results:

29. Since the force of resistance is in the opposite direction of the displacement the work done by this force is given by Wnc = -Fd where F is the magnitude of the resistive force. The potential energy of the rock is given by U = mgh relative to the bottom of the pond. The kinetic energy of the rock can be calculated from the work energy theorem K = Wnc - DU and the total energy is E = U + K.

For d = 0:

Wnc = -4.10 N (0) = 0
U = (1.75 kg)(9.81 m/s2)(1.00) = 17.2 J
K = 0 - 0 = 0
E = 17.2 J + 0 = 17.2 J

For d = 0.500 m:

Wnc = -4.10 N (0.500 m) = -2.05 J
U = (1.75 kg)(9.81 m/s2)(0.500) = 8.58 J
K = -2.05 J - (8.58 J - 17.17 J) = 6.54 J
E = 8.58 J + 6.54 J = 15.1 J

For d = 1.00 m:

Wnc = -4.10 N (1.00 m) = -4.10 J
U = (1.75 kg)(9.81 m/s2)(0) = 0
K = -4.10 J - (0 J - 17.2 J) = 13.1 J
E = 0 J + 13.1 J = 13.1 J

49. Coming off the slide, the person becomes a projectile launched horizontally. The landing site of such a projectile is determined by x = vxt with . Therefore,


We can relate this velocity to the height of the slide using energy conservation:


Plugging in the result for v2 gives

.

Selected Solutions by David Reid, Eastern Michigan University. ©2002 by Prentice Hall, Inc.


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