A box is dragged with a force of 115 N up a ramp a distance of 3 m. If the force makes an angle of 35 degrees with the ramp and the ramp makes an angle of 20 degrees with the ground, how much work is done?
To determine the work done in this scenario, we need to calculate the component of the force that is acting in the direction of the displacement of the box.
Work is calculated by multiplying the magnitude of the force by the magnitude of the displacement, as well as the cosine of the angle between the force and the displacement.
First, find the component of the force that is acting in the direction of the displacement. This can be found using the formula:
F_parallel = F * cos(theta)
where F is the given force and theta is the angle between the force and the direction of motion.
F_parallel = 115 N * cos(35 degrees)
F_parallel = 115 N * 0.8192
F_parallel ≈ 94 N
Next, calculate the displacement of the box along the ramp. Since the ramp makes an angle of 20 degrees with the ground, the vertical displacement is given by:
vertical displacement = distance * sin(theta)
vertical displacement = 3 m * sin(20 degrees)
vertical displacement ≈ 1.02 m
Finally, calculate the work done:
Work = F_parallel * displacement
Work = 94 N * 1.02 m
Work ≈ 95.88 Joules
Therefore, approximately 95.88 Joules of work is done in dragging the box up the ramp.