Calculating Horizontal Force Needed to Pull Wheel

[formulajoe]

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.
?

 

[Njorl]

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 vertical 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

 

[himanshu121]

The vertical 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

 

[himanshu121]

We should look for conservation of Energy

 

[formulajoe]

torque = F * R, but where do i factor in the H?

 

[himanshu121]

nope torque is not FR here

 

[formulajoe]

is torque even used in this problem?

 

[himanshu121]

$$Fsin \theta R=I \alpha$$

 

[Njorl]

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 vertical 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

 

[himanshu121]

The wheel will roll over the step when the reactive force from the step has a vertical component equal and opposite to the gravitaional effect upon the wheel.

How that is going to help to solve the prob,

 

[formulajoe]

im stuck at F*sintheta = m * a now.
how do i factor in the H?

 

[himanshu121]

$$Fsin\theta r = i \frac{d\omega}{dt}$$
$$FRsin\theta d\theta=\omega I d\omega$$

solving this from fig uget

$$\frac{I\omega^2}{2}=\frac{FRH}{\sqrt{R^2+(R-H)^2}}$$

 

[himanshu121]

Apply Conservation of Energy

$$F=\frac{mg \sqrt{R^2+(R-H)^2}}{R}$$

 

[NateTG]

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
$$\tau_F=-(r-h)F$$
(negative because it is clockwise)
$$\tau_G=mg\sqrt{R^2-(R-H)^2}$$
and
$$\tau_F>-\tau_G$$
so
$$F > \frac{mg \sqrt{2RH-H^2}}{R-H}}$$

 

[himanshu121]

Sorry i lost NateTG is correct