A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37° above the horizontal.How much work does gravity do on the box during this process?
A)-1100 J
B)-110 J
C)-140 J
D)-180 J
E)120 J

Question

Quizplus · Accepted Answer

Gravity does no work on the box because the force of gravity is perpendicular to the displacement of the box. The work done on the box is equal to the work done by the person pulling the box up the ramp against gravity. The calculation for this work is:

Work = force x distance x cos(theta)

where force is the component of the force vector that is parallel to the displacement, distance is the distance over which the force is applied, and theta is the angle between the force vector and the displacement.

In this case, the force is equal to the weight of the box (30 N) times the sin of the angle of the ramp (37°) because this is the component of the weight that is parallel to the ramp. The distance is equal to the length of the ramp (6.0 m), and cos(theta) is equal to the cosine of the angle of the ramp (37°). Plugging in these values, we get:

Work = (30 N) x (sin 37°) x (6.0 m) x (cos 37°) ≈ 110 J

Therefore, the correct answer is B.

A 30-N Box Is Pulled Upward 6