# Pushing a Wheel over a Bump

1. Jul 15, 2012

### PrestonBlake

1. The problem statement, all variables and given/known data

You have a wheel of mass m and radius R you're trying to push it onto a block of height h that it's next to. Find the minimum force F that will let you do this. F is completely horizontal and acts upon the center of the wheel.

2. Relevant equations

I'm trying to solve this by pretending the wheel is a lever attached to the edge of the block. It has two forces acting on it F and gravity. To find the minimum force I assume F*sin(theta)*R=G*Sin(theta)*R

3. The attempt at a solution

I believe that the line from the part where the wheel touches the block to the center of the wheel makes a degree of arcsin(1-h/r) Then I try to calculate the degree each force makes with the perpendicular of the imaginary lever to get g*m*cos(Pi/2-arcsin(1-h/r))==F*cos(arcsin(1-h/r)). Then I solve for F and get a wrong answer.

2. Jul 15, 2012

### ehild

3. Jul 15, 2012

### PrestonBlake

Are you sure? It's a given that F is pushing on the center and I'm assuming that gravity is working on the center of mass, which should be the same as the center.

4. Jul 15, 2012

### azizlwl

Use the point of contact between wheel and the block as fulcrum.
Use moments to solve the problem.

5. Jul 15, 2012

### PrestonBlake

That's what I did, but apparently I messed up the trig on my way to the answer.

6. Jul 15, 2012

### ehild

Gravity is vertical, the force is horizontal. You use the touching point between ball and block as pivot point. The arms are not equal.

ehild

7. Jul 15, 2012

### azizlwl

Use phytagoras theorem to find arms length.
For using trig function,
Weight, it should be mgCosθ.R

8. Jul 15, 2012

### PrestonBlake

Thanks, it turns out I had switched the angle of gravity with the angle of the force.

9. Jul 15, 2012

### PrestonBlake

As a second question, what would the arm length be if the force was acting at the top of the wheel instead of at the middle.