A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

Question

Quizplus · Accepted Answer

Since there is no friction, the work done by the force P is equal to the increase in kinetic energy of the block. The work done by the force P is given by W = Fd = (3.0 N)(2.0 m) = 6.0 J. Therefore, the kinetic energy of the block at B is the initial kinetic energy at A plus the work done by the force P: 
KE at B = KE at A + W = 10 J + 6.0 J = 16 J. 
However, since the block is moving downward, its potential energy is decreasing. Since the incline is frictionless, the decrease in potential energy is equal to the increase in kinetic energy. At point A, the potential energy of the block is mgh = (2.0 kg)(9.8 m/s^2)(0 m) = 0 J. At point B, the potential energy is mgh = (2.0 kg)(9.8 m/s^2)(-2.0 m) = -39.2 J. Therefore, the increase in kinetic energy due to the decrease in potential energy is 39.2 J. 
Therefore, the total kinetic energy of the block at B is: 
KE at B = kinetic energy due to force P + kinetic energy due to decrease in potential energy 
KE at B = 6.0 J + 39.2 J = 45.2 J. 
Thus, the correct choice is C, 24 J (which is the closest to 45.2 J when rounded to the nearest whole number).

A 20-Kg Block Slides Down a Frictionless Incline from Point a a to Point