What force is needed to lift a wheel over a bump with given mass and radius?

[Julia123]

Homework Statement

The question is as follows:
How much force should I apply if i want to have a wheel of mass 2kg and radius R to pass over a step with height h, where R is twice as big as h.
I attached a picture of the problem for reference.

Homework Equations

I am not sure but I think I should be using torque and possibly moment of Inertia to solve this problem.

The Attempt at a Solution

I don't know how to approach the problem and would really appreciate a nudge in the right direction. Thank you in advance for any and all help!

 

[Doc Al]

Here's a nudge: Torque is the way to go. What will you take as your pivot point for calculating torque?

 

[Julia123]

The pivot point must be the corner of the step right? But what do I do from there? How can I know that the force is perpendicular if the wheel is spinning over the bump and the angle is changing?

 

[Doc Al]

The pivot point must be the corner of the step right?

That works.

How can I know that the force is perpendicular if the wheel is spinning over the bump and the angle is changing?

The applied force is horizontal, per the diagram. What other forces act to create a torque about the pivot?

 

[Julia123]

the force of gravity also works to create a torque about the pivot. The moment of inertia works against the angular acceleration of the wheel. Do I have to account for both of these things in the torque equation?

 

[Doc Al]

the force of gravity also works to create a torque about the pivot.

Good. In what direction is the torque due to gravity? The applied force must at least balance that torque in order to lift up the wheel.

The moment of inertia works against the angular acceleration of the wheel. Do I have to account for both of these things in the torque equation?

No, forget about angular acceleration. Just consider torque. You are looking for the minimum applied force to just barely lift the thing over the bump.