A man pushes a 200 N crate up a frictionless incline with a slope of 20 degrees. The crate is raised by 4 m as

shown. Assuming the crate moves at constant speed, what is the work done by the man?.

I know Work = Force x Displacement. The answer is 800 N. Why is the displacement 4 m and not the hypotenuse of the ramp (4/sin20)?

The increase in gravitational potential energy

= m g h
where h is the HEIGHT change, the increase in distance from the center of the earth.
Work = distance times force IN THE DIRECTION OF MOTION
200 * 4 = 800 Joules
alternatively force component up slope * 4/sin 20
= 200 sin 20 * 4/sin 20 = 800 :)

To calculate the work done by the man, you are correct in using the formula W = F * d, where W is the work done, F is the force applied, and d is the displacement.

In this scenario, the force applied by the man is 200 N, and the crate is raised by 4 m. However, it is important to understand that the displacement you need to use in this case is the vertical displacement, which is directly upwards, not the hypotenuse of the ramp.

When the crate moves up the incline, the force applied by the man is used to counteract the weight of the crate and to lift it vertically. The vertical displacement of the crate is 4 m because it is lifted straight up. The distance along the incline (the hypotenuse) is not considered because the force applied is orthogonal to the incline.

In this case, the displacement is measured in the same direction as the force, which is vertically upwards. So, the displacement to consider is the vertical height of 4 m, and the work done by the man is given by:

Work = Force * Displacement = 200 N * 4 m = 800 N.

Therefore, the work done by the man is 800 N.