Physics C - Rotational motion/forces

[dominus96]

Homework Statement

An amusement park ride consists of a rotating cylinder with rough canvas walls. The rider enters the cylinder and stands on the floor as the cylinder starts spinning, and as it spins, the floor lowers but the rider stays against the wall and does not slide down with it. The mass of the rider is 50 kg, the radius of the cylinder is 5 meters, the rotational speed is 2 radians/second, and the coefficient of static friction is 0.6.

a) Calculate the upward force that allows the rider from falling when the floor lowers, and state what provides that force.

b) At the same rotational speed, would a person of 100 kg slide down the wall? Explain.

Homework Equations

F=ma
F_centripetal = mv²/r

The Attempt at a Solution

I drew a free-body diagram and got 500 N for weight, which would mean 500 N for friction since they are in opposite directions and the rider is in equilibrium. The normal force is 833 N.

For part a) I think the answer is the frictional force, but I don't know the exact reason.

Part b) I would assume that it won't affect it. Am I right?

 

[dominus96]

bump can someone help me?

 

[baba89]

Hello! As a physicist, I can provide a response to your question regarding rotational motion and forces.

For part a), you are correct in stating that the upward force preventing the rider from falling is the frictional force. This is because as the cylinder rotates, the rider experiences a centripetal force pulling them towards the center of the cylinder. This force is balanced by the frictional force acting in the opposite direction, providing the necessary centripetal force to keep the rider in equilibrium and prevent them from sliding down the wall.

For part b), the mass of the rider does not affect the frictional force in this situation. This is because the frictional force depends on the coefficient of static friction and the normal force, both of which remain constant regardless of the rider's mass. Therefore, a person of 100 kg would also not slide down the wall, as long as the coefficient of static friction and the rotational speed remain the same.

I hope this helps clarify your understanding of rotational motion and forces in this scenario. Keep up the good work in your studies of physics!