A box with mass $ m = 76 \, \text{kg} $ is being pulled by a constant force $ F = 175 \, \text{N} $ at an angle of $ \theta = 34^\circ $. The initial speed of the box is zero. Write an expression for the work done by the force.

A. $ W = 175 \, \text{J} $

B. $ W = 175 \cos(34^\circ) $

C. $ W = 175 \sin(34^\circ) $

D. $ W = 175 \cos(34^\circ) \sin(34^\circ) $

The correct expression for the work done by the force on a box is W = 175 cos(34°) multiplied by the displacement, assuming no friction and the force is applied at an angle of 34° relative to the horizontal.

Explanation:

the work done by a force on a box weighing 76 kg that is being pulled by a constant force of 175 N at an angle of 34°. Work is defined in physics as the product of the force acting in the direction of displacement and the displacement itself. Considering that the force is being applied at an angle above the horizontal, only the horizontal component of the force acts in the direction of the displacement. This horizontal component is given by F cos(θ), where F is the force applied and θ is the angle of the force relative to the horizontal.

To express the work done by the force, the correct formula based on this concept would be W = F d cos(θ), where W is work, F is the force magnitude, d is the distance through which the force acts, and θ is the angle between the force and the direction of the displacement. Therefore, among the given options, the correct expression for the work done by the force is (b) W = 175 cos(34°) multiplied by the displacement, assuming that the angle given is with respect to the horizontal and ignoring friction and air resistance. Note that the expression for work is not complete until you include the displacement, which is not provided in the question.