A rear wheel on a Formula 1 racing car has a mass of 3.2kg and aradius of 0.42m.

Question

A rear wheel on a Formula 1 racing car has a mass of 3.2kg and aradius of 0.42m. Amechanic is rolling the wheel towards a step atthe back of the workshop. Determine:
i) the minimum horizontal force (F) needed to be app;iedthrough the axle (center) of the wheel to just start rolling overthe step if it is 6cm tall.
ii) the minimum horizontal force needed to be applied at thetop of the wheel to just start it rolling over the same step.
i) the minimum horizontal force (F) needed to be app;iedthrough the axle (center) of the wheel to just start rolling overthe step if it is 6cm tall.
ii) the minimum horizontal force needed to be applied at thetop of the wheel to just start it rolling over the same step.

Explanation / Answer

A good start to any problem is to draw a diagram: Let d be the horizontal distance from a vertical radius of the wheel to the point where the wheel meets the step. If h is the height of the step then the following relation holds d^2 = R^2 - (R - h)^2 d = [.42^2 - (.42 - .06)^2]^1/2 = 21.6 cm = .216 m Clockwise torque = F * (R - h) Counter-clockwise torque = m g d F = m g d / (R - h) = 3.2 * 9.8 * .216 / (.36) = 18.8 N For the second part Clockwise torque = F * (2 R - h) The Counter-clockwise torque remains the same

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