Optimizing Force for Pushing Wheel over Bump

[PrestonBlake]

Homework Statement

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.

Homework 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

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.

 

[ehild]

Homework 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


The lever arm of gravity is not the same as that of the force F.

ehild

 

[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.

 

[azizlwl]

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

 

[PrestonBlake]

Use the point of contact between wheel and the block as fulcrum.

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

 

[ehild]

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.

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

 

[azizlwl]

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

 

[PrestonBlake]

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

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

 

[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.