A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?
A) 2.7 J
B) 1.0 J
C) 2.2 J
D) 1.6 J
E) 3.2 J

Question

A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B? 
A) 2.7 J 
B) 1.0 J 
C) 2.2 J 
D) 1.6 J 
E) 3.2 J

Quizplus · Accepted Answer

The work done on the block by the force P between A and B is equal to the change in kinetic energy of the block, so
W = ΔKE = KEb - KEa = 5.6 J - 4.0 J = 1.6 J
However, this work is done against the force of friction, so the actual work done by force P is
W = Fd - f d = (5.4 N)(0.5 m) - (1.2 N)(0.5 m) = 2.1 J
Therefore, the best choice is C (2.2 J), which is the closest answer choice to the calculated value of 2.1 J.

A Block Is Pushed Across a Rough Horizontal Surface from Point