A particle that is subjected to a variable force travels a distance of 20 m in a straight line in the same direction as the force. The force varies as follows:
First, 5.0 m and F = 0
Next, 5.0 m and F = 3.0 N
Next, 5.0 m and F = 6.0
Last, 5.0 m and F decreases uniformly from 6.0 N to zero
What was the total work done by this force during the full 20-m trip?
A) 15 J
B) 30 J
C) 45 J
D) 60 J
E) 75 J

Question

Quizplus · Accepted Answer

For the first 5 m, force is 0 N, hence no work is done.

For the next 5 m, force is constant at F = 3.0 N, hence work done is W = F*d = 3.0 N * 5.0 m = 15 J.

For the next 5 m, force is constant at F = 6.0 N, hence work done is W = F*d = 6.0 N * 5.0 m = 30 J.

For the last 5 m, force is changing uniformly from 6.0 N to 0 N. The average force during this distance is (6.0 N + 0 N)/2 = 3.0 N. Therefore, work done during this distance is W = F_avg * d = 3.0 N * 5.0 m = 15 J.

Therefore, the total work done by the force during the full 20-m trip is: 0 J + 15 J + 30 J + 15 J = 60 J.

The correct answer is D, 60 J.

A Particle That Is Subjected to a Variable Force Travels