The drawing shows a bicycle wheel resting against a small step whose height is h = 0.125 m. The weight and radius of the wheel are W = 23.1 N and r = 0.330 m, respectively. A horizontal force vector F is applied to the axle of the wheel. As the magnitude of vector F increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happens?

Question

The drawing shows a bicycle wheel resting against a small step whose height is h = 0.125 m. The weight and radius of the wheel are W = 23.1 N and r = 0.330 m, respectively. A horizontal force vector F is applied to the axle of the wheel. As the magnitude of vector F increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happens?
N

Damon · Accepted Answer

Distance axle above step edge = .33 - .125 = .205

Angle T is angle between straight down from Axle and the top edge of the step
so
cos T = .205/.33
T = 10.58 deg
sin T = .184

Take moments about the top edge of the step.
F * .205 clockwise (my step is on the right)

m g * .33 sin T counterclockwise
distance of wheel axle above step
but m g =23.1 N
so
23.1 * .33 * .184 = .205 F
F = 6.83 N

dakota22 · Answer

Thank you so much for your time and help!