Question

A wheel and axle on a bicycle are designed with an axle radius of 0.5 feet and a wheel radius of 2 feet . If a force of 200 pounds is applied to the axle, what is the maximum output force of the bike wheel?

a) 1,200 lb
b) 50 lb
c) 200 lb
d) 800 lb

Answer 1

Answer: The answer is 50 lb! :)

Answer 2

The maximum output force of the bike wheel is 50lb

In order to calculate the maximum output force of the bike wheel, we will use the formula:

$\frac{R}{r} =\frac{F}{f}$

R and r are the radii on the axle and wheel respectively

F and f are the respective force applied

Given the following parameters

R = 2 feet

r = 0.5 ft

F = 200

Substitute the given parameters into the formula to have:

$\frac{2}{0.5} =\frac{200}{f}\\2f = 200 * 0.5\\2f = 100\\f = 50lb$

Hence the maximum output force of the bike wheel is 50lb

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