To push a 26.0 kg crate up a frictionless incline, angled at 25.0° to the horizontal, a worker exerts a force of 209 N parallel to the incline. As the crate slides 1.9 m, how much work is done on the crate by (a) the worker's applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) What is the total work done on the crate?

(a) W = + 397.1 J

(b) W = - 204.6 J

(c) W = 0

(d) W = + 192.5 J

Explanation:

Work (W) is defined as the product of force (F) by the distance (d) the body travels due to this force.:

W = F*d Formula (1)

The forces that perform work on an object must be parallel to its displacement.

The forces perpendicular to the displacement of an object do not perform work on it.

The work is positive (W+) if the force has the same direction of movement of the object.

The work is negative (W-) if the force has the opposite direction of the movement of the object.

Problem development

(a) Work performed by the worker's applied force on the box.

W = 209 N * 1.9 m = + 397.1 J

(b) Work performed by the gravitational force on the crate

We calculate the weight component parallel to the displacement of the box:

We define the x-axis in the direction of the inclined plane, 25.0° to the horizontal.

We define the y-axis and in the direction of the plane perpendicular to the inclined plane.

W = m*g=26*9.8 = 254.8N : total box weight

Wx = W*sen25.0° = 254.8*sen25.0° = 107.68 N

W = - Wx * d = 107.68 N * 1.9 m = - 204.6 J

(c) Work performed by normal force (N) exerted by the incline on the crate

The force N is perpendicular to the displacement, then:

W=0

(d) Total work done on the crate

W = 397.1 J - 204.6 J

W = 192.5 J