Question

Two people want to raise a block by a height h, and have been given a rope and an extendable ramp to help them with the task. The coefficient of kinetic friction between the block and the ramp is μk. Assume that they use the rope to always pull the block up parallel to the surface of the ramp and that it moves with constant velocity.

(a) The first person is a weighlifting enthusiast, so they’re interested in maximizing the force needed. What angle should they set the ramp at?

Answer 1

The ramp should be set at an angle near but not exceeding 90 degrees to maximize the force needed to raise a block, balancing practical considerations with maximizing the gravitational component.

Step-by-step explanation:

The person interested in maximizing the force needed to raise the block should set the ramp at an angle where the force due to gravity parallel to the ramp surface is greatest. This occurs when the ramp is set at an angle where sin(θ) is maximized, which is at 90 degrees. However, anything beyond a certain practical limit will turn the ramp into a vertical wall, which is not realistic. Thus, setting the ramp at or just below 90 degrees will require the greatest force to overcome both gravity and the kinetic friction between the block and the ramp. It's important to note that in practical contexts, a ramp approaching vertical would not be considered a ramp and would not be feasible for lifting an object using a rope.