Find minimum force to raise wheel

In summary, the necessary force F to raise a wheel of mass M and radius R over a step of height H can be calculated using the equation F = [mg*SQRT(2RH-H^2)]/r-h, where mg is the force of gravity and SQRT(2RH-H^2) is derived from the sum of torque. Additionally, the correct lever arm for the weight should be perpendicular to the line of action of the force.
  • #1
vu10758
96
0
What minimum force F applied horizontally at the axle of the wheel is necessary to raise the wheel of mass M and radius R over a step of height H. A picture for this is at

http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=128765607&imageID=1460005538


The answer key says that the correct answer is F =[mg*SQRT(2RH-H^2)]/r-h

I know that mg is gravity so the force of gravity plays a role here. I don't know the direction of friction because F is pointing right, but the object also rotates clockwise. Friction would resist the sliding but would contribute to the rotation.

I know torque is the cross product of R and F. I have no idea though why we have SQRT(2RH-H^2). I don't know what to do. Am I suppose to work with torque somehow?
 
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  • #2
Take moment about the contact point, and use a force with unknown direction for the reaction at the contact point.
 
  • #3
I am not sure about this...is the moment of inertia with respect to the contact point MR^2 + R^2 with the parallel axis theorem? I know that whatever force the wheel pushes against the contact point, the same force will push the wheel back. But I am not sure about how to find that force for the reaction.
 
  • #4
By moment, i meant sum of torque, and consider Normal force = 0.
 
  • #5
With net torque, I have mg*R + F(R-H).

So F = mg*R/(R-H)

From the way it seems, I got the F(R-H) part right, but mg*R is still not quite right. HOw do I get SQRT(2RH-H^2)?
 
  • #6
vu10758 said:
With net torque, I have mg*R + F(R-H).

So F = mg*R/(R-H)

From the way it seems, I got the F(R-H) part right, but mg*R is still not quite right. HOw do I get SQRT(2RH-H^2)?

Your lever arm for the weight is wrong, REMEMBER THE LEVER ARM IS PERPENDICULAR TO THE LINE OF ACTION OF THE FORCE.
 

Related to Find minimum force to raise wheel

1. What is the purpose of finding the minimum force to raise a wheel?

The purpose of finding the minimum force to raise a wheel is to determine the minimum amount of force needed to lift a wheel off the ground, taking into account factors such as weight, friction, and angle of incline. This information is important for designing and optimizing mechanisms that rely on lifting or rotating wheels, such as car jacks or pulley systems.

2. How is the minimum force to raise a wheel calculated?

The minimum force to raise a wheel can be calculated using the equation F = mg/(cosθ + μsinθ), where F is the minimum force, m is the weight of the wheel, g is the acceleration due to gravity, θ is the angle of incline, and μ is the coefficient of friction. This equation takes into account the forces acting against the wheel, such as gravity and friction, to determine the minimum force needed to overcome them and lift the wheel.

3. What factors affect the minimum force to raise a wheel?

The minimum force to raise a wheel is affected by several factors, including the weight of the wheel, the angle of incline, and the coefficient of friction between the wheel and its surface. Other factors such as air resistance and the design of the wheel may also play a role in determining the minimum force.

4. How does the angle of incline affect the minimum force to raise a wheel?

The angle of incline has a significant impact on the minimum force needed to raise a wheel. As the angle increases, the force required to lift the wheel also increases due to the increased effect of gravity and friction. At a certain point, known as the critical angle, the force needed to lift the wheel becomes infinite, meaning the wheel cannot be lifted at that angle.

5. What are some real-world applications of finding the minimum force to raise a wheel?

Some real-world applications of finding the minimum force to raise a wheel include designing car jacks, pulley systems, and other lifting mechanisms. This information is also useful in industries such as construction and transportation, where heavy objects need to be lifted or moved using various mechanisms. Additionally, understanding the minimum force to raise a wheel can help prevent accidents and ensure the safe and efficient use of lifting equipment.

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