Final answer:
The work done by gravity as the box slides down the inclined plane is 40 Joules, as the force component parallel to the plane is 20 N and the box moves 2 m along the plane.
Step-by-step explanation:
The question involves calculating the work done by the force of gravity as a box slides down an inclined plane. The work done by gravity is given by the formula W = F * d * cos(\theta), where F is the force due to gravity acting on the object, d is the distance moved along the direction of the force, and \theta is the angle between the force and the direction of movement. Since the box is moving along the plane, only the component of the gravitational force acting parallel to the direction of the movement does work.
In this case, the force due to gravity, F, can be found by multiplying the weight of the box (40 Newtons) by the sine of the angle of the incline since F = mg * sin(\theta). Therefore, the component of the gravitational force acting along the incline is 40 * sin(30°) or 20 N. The distance moved by the box, d, is 2 meters, and the angle between the force and the direction of movement is 0 degrees, since they are parallel, and cos(0) is 1.
The work done by gravity is thus W = 20 N * 2 m * 1, which equals 40 Joules. So, the correct answer is c. 40 J.