How Much Force to Overcome a Step with a Wheel?

[Eagle Eyes]

Homework Statement

A wheel of radius R and mass M is dragged over a step of height h by force F applied horizontally at its center. What is the maximum value of F required so that the wheel climbs over the step? (Hint: wheel climb is equivalent to a rotation around the point of contact with the step.)

Homework Equations

Not available.

The Attempt at a Solution

I have no idea how to start this. But i would use potential energy perhaps?

 

[LowlyPion]

Homework Statement

A wheel of radius R and mass M is dragged over a step of height h by force F applied horizontally at its center. What is the maximum value of F required so that the wheel climbs over the step? (Hint: wheel climb is equivalent to a rotation around the point of contact with the step.)

Homework Equations

Not available.

The Attempt at a Solution

I have no idea how to start this. But i would use potential energy perhaps?

You're going to want to consider the Σ Torques > 0 needed to pivot over the edge of the step as the hint suggests.

 

[nlightner]

As a scientist, it is important to approach problems with a systematic and analytical mindset. In this case, we can use the principle of conservation of energy to solve for the maximum force required for the wheel to climb over the step.

First, let's define the system and its initial and final states. The system consists of the wheel and the step, and the initial state is when the wheel is at rest on the ground before the step. The final state is when the wheel has climbed over the step and is at rest on the other side.

Next, we can use the equation for gravitational potential energy, U = mgh, to determine the potential energy of the wheel at the initial and final states. At the initial state, the potential energy is zero since the wheel is at ground level. At the final state, the potential energy is mgh, where m is the mass of the wheel, g is the acceleration due to gravity, and h is the height of the step.

Since energy is conserved, the change in potential energy must be equal to the work done by the applied force, F. Therefore, we can set up the following equation:

mgh = Fh

Solving for F, we get:

F = mg

This means that the maximum force required for the wheel to climb over the step is equal to the weight of the wheel, which is mg. This makes sense since the wheel needs to overcome its weight in order to climb the step.

In conclusion, the maximum force required for the wheel to climb over the step is mg, where m is the mass of the wheel and g is the acceleration due to gravity. This can also be seen as the minimum force required to lift the wheel off the ground.