Calculating Horizontal Force Needed to Pull Wheel

In summary, to pull a wheel of radius R and mass M over a step of height H, a force is needed that is supplied at the center of the wheel. The wheel will roll over the step when the reactive force from the step has a verticle component equal and opposite to the gravitaional effect upon the wheel.
  • #1
formulajoe
177
0
what minimum horizontal force is needed to pull a wheel of radius R and mass M over a step of height H. force is supplied at center of wheel.
?
 
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  • #2
Draw yourself a force diagram. Just to get you started right, make the step height smaller than R, otherwise no force will be sufficient. The verticle component of the force exerted by the step upon the wheel must counteract gravity, so that it lifts off of the ground.

You might also want to show that the process "runs away". As the wheel climbs over the step, less force is needed. This ensures that you don't have to worry about climbing partly up the step and rolling back down.

Njorl
 
  • #3
The verticle component of the force exerted by the step upon the wheel must counteract gravity, so that it lifts off of the ground.

Given force is horizontal
 
  • #4
We should look for conservation of Energy
 
  • #5
torque = F * R, but where do i factor in the H?
 
  • #6
nope torque is not FR here
 
  • #7
is torque even used in this problem?
 
  • #8
[tex]Fsin \theta R=I \alpha[/tex]
 

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  • #9
Originally posted by himanshu121
Given force is horizontal

Yes, but reactive forces are not.

The applied forces are a horizontal force upon the axis, and gravity. The reactive forces are from the ground, and the step. The wheel will roll over the step when the reactive force from the step has a verticle component equal and opposite to the gravitaional effect upon the wheel. This will mean the ground supplies no force, because the wheel will stop touching the ground.

Njorl
 
  • #10
The wheel will roll over the step when the reactive force from the step has a verticle component equal and opposite to the gravitaional effect upon the wheel.

How that is going to help to solve the prob,
 
  • #11
im stuck at F*sintheta = m * a now.
how do i factor in the H?
 
  • #12
[tex]Fsin\theta r = i \frac{d\omega}{dt}[/tex]
[tex]FRsin\theta d\theta=\omega I d\omega[/tex]

solving this from fig uget

[tex]\frac{I\omega^2}{2}=\frac{FRH}{\sqrt{R^2+(R-H)^2}}[/tex]
 
  • #13
Apply Conservation of Energy

[tex]F=\frac{mg \sqrt{R^2+(R-H)^2}}{R}[/tex]
 
  • #14
Do the torque calculations about the edge of the step. Torque due to the normal force is zero. That leaves torque due to gravity, and torque due to the applied force which must be larger.
I get
[tex]\tau_F=-(r-h)F[/tex]
(negative because it is clockwise)
[tex]\tau_G=mg\sqrt{R^2-(R-H)^2}[/tex]
and
[tex]\tau_F>-\tau_G[/tex]
so
[tex]F > \frac{mg \sqrt{2RH-H^2}}{R-H}}[/tex]
 
  • #15
Sorry i lost NateTG is correct
 

1. How do you calculate the horizontal force needed to pull a wheel?

To calculate the horizontal force needed to pull a wheel, you will need to know the weight of the wheel, the coefficient of friction, and the angle between the ground and the direction of motion. The formula for calculating this force is F = μmgcosθ, where F is the force, μ is the coefficient of friction, m is the mass of the wheel, g is the acceleration due to gravity, and θ is the angle.

2. What is the coefficient of friction?

The coefficient of friction is a measure of the amount of friction between two surfaces in contact. It is represented by the symbol μ and is a dimensionless number. A higher coefficient of friction means there is more resistance to motion between the two surfaces.

3. How does the weight of the wheel affect the horizontal force needed to pull it?

The weight of the wheel directly affects the horizontal force needed to pull it. The heavier the wheel, the greater the force needed to overcome its inertia and move it horizontally. This is represented in the formula as the variable m (mass).

4. What is the significance of the angle in the formula for calculating the horizontal force?

The angle, represented by θ in the formula, is the angle between the ground and the direction of motion. This angle determines the direction of the force needed to pull the wheel. If the angle is 0 degrees, meaning the wheel is being pulled along a flat surface, the horizontal force needed will be equal to the weight of the wheel multiplied by the coefficient of friction. However, as the angle increases, the horizontal force needed will also increase.

5. How can this calculation be useful in real-life situations?

Knowing how to calculate the horizontal force needed to pull a wheel can be useful in various real-life situations. For example, it can help in determining the force needed to pull a cart or a sled, or in designing machinery that requires pulling or pushing of heavy objects. It can also be useful in understanding the physics behind everyday activities, such as pulling a suitcase or pushing a shopping cart.

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