A solid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. It is ajar and at rest. A ball with a mass of 500 g is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. The ball rebounds with a speed of 16.0 m/s along the same line. How much energy is lost in the process?
A) 29.8 J
B) 16.3 J
C) 14.9 J
D) 12.7 J
E) 4.79 J

Question

Quizplus · Accepted Answer

Explanation:The change in kinetic energy of the ball is:$$\Delta K = K_f - K_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$$$= \frac{1}{2}(0.500 	ext{ kg})(16.0 	ext{ m/s})^2 - \frac{1}{2}(0.500 	ext{ kg})(20.0 	ext{ m/s})^2$$$$= -14.9 	ext{ J}$$The negative sign indicates that the kinetic energy of the ball has decreased.The energy lost in the process is equal to the change in kinetic energy of the ball:$$E_{lost} = |\Delta K| = 14.9 	ext{ J}$$

A Solid Wood Door, 90