Question

A 54-kg box is being pushed a distance of 7.1 m across the floor by a force Upper POverscript right-arrow EndScripts ? whose magnitude is 188 N. The force Upper POverscript right-arrow EndScripts ? is parallel to the displacement of the box. The coefficient of kinetic friction is 0.23. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force. (a) WP = (b) Wf = (c) Wmg = (d) WN =

Answer 1

The four forces acting on the box are a) the pushing force, b) the frictional force of the floor, c) the weight of the own box, and d) the normal force of the floor back up on the box. Recall that work W is defined as a force F through a distance d, or . Also recall that work is positive when the force is acting in the same direction as the direction of the movement of the box.

(a)

Find the work done by the pushing force. We're told that , and the distance it's pushed through is . Plug these into to find the work.

Since the pushing force is in the same direction that box is moving, the work done by the pushing force is +1335 J.

(b)

The force of friction is equal to , where is the coefficient of friction and N is the normal force of the floor on the box. Using Newton's 2nd law, since there is no vertical motion (the box is sliding across the floor, not falling down through the floor) than the normal force pushing up on the box must be equal to weight of the box, or where m is the mass of the box and g is the acceleration of gravity.

Plug , , , , and into to find the work done by friction.

Since friction is acting to opposite the motion of the box, the work done by friction is -864.2 J.

(c)

The work done by gravity is equal to the force of gravity through the distance that the box moves in the same direction. Gravity in acting vertically though and the box is moving horizontally - so gravity does no work, .

(d)

Similarly, the normal force from the floor pushing up on the box does no work because there is no motion in the vertical direction. The normal force acts vertically on the box, but the box is only moving horizontally. Because the normal force isn't acting in the direction of the motion of the box, .