Question

a wheel and axle on a bicycle are designed with an axle radius of 0.125 meters and a wheel radius of 0.5 meters. if a force of 800 newtons is applied to the axle, what is the maximum output force of the bike wheel? (1 point) 100 n 800 n 200 n 3,200 n

Explanation:

Step1: Apply the principle of wheel - and - axle

The principle of wheel - and - axle is \(F_1\times r_1 = F_2\times r_2\), where \(F_1\) is the input force, \(r_1\) is the radius of the axle, \(F_2\) is the output force, and \(r_2\) is the radius of the wheel.
We are given \(F_1 = 800\space N\), \(r_1=0.125\space m\), and \(r_2 = 0.5\space m\). We need to solve for \(F_2\).
From \(F_1\times r_1=F_2\times r_2\), we can express \(F_2=\frac{F_1\times r_1}{r_2}\)

Step2: Substitute the values

Substitute \(F_1 = 800\space N\), \(r_1 = 0.125\space m\), and \(r_2=0.5\space m\) into the formula \(F_2=\frac{F_1\times r_1}{r_2}\)
\(F_2=\frac{800\times0.125}{0.5}\)
First, calculate \(800\times0.125 = 100\)
Then, \(\frac{100}{0.5}=200\space N\)

Answer:

C. \(200\space N\)