In the figure,a 700-kg crate is on a rough surface inclined at 30°.A constant external force P = 5600 N is applied horizontally to the crate.As the force pushes the crate a distance of 3.00 m up the incline,the speed changes from 1.40 m/s to 2.50 m/s.How much work does gravity do on the crate during this process?
A) -10,300 J
B) -3400 J
C) +10,300 J
D) +3400 J
E) zero

Question

In the figure,a 700-kg crate is on a rough surface inclined at 30°.A constant external force P = 5600 N is applied horizontally to the crate.As the force pushes the crate a distance of 3.00 m up the incline,the speed changes from 1.40 m/s to 2.50 m/s.How much work does gravity do on the crate during this process? 
A) -10,300 J 
B) -3400 J 
C) +10,300 J 
D) +3400 J 
E) zero

Quizplus · Accepted Answer

To find the work done by gravity on the crate, we need to find the change in potential energy. As the crate moves up the incline, its potential energy increases.

ΔPE = mgh

where m is the mass of the crate, g is the acceleration due to gravity, and h is the change in height. Since the crate only moves along the incline, we can use the component of gravity parallel to the incline.

mgh = mg sin θ * d = (700 kg) * (9.81 m/s²) * sin 30° * 3.00 m = 10,300 J

Since the angle between the force and displacement is not 0° or 180°, the work done by gravity is negative (i.e. gravity does negative work on the crate).

Therefore, the answer is A) -10,300 J.

In the Figure,a 700-Kg Crate Is on a Rough Surface