Question

the mechanical advantage of the wheel - and - belt assembly shown in the illustration is $\frac{1}{3}$. what is the diameter of the driver wheel? a 2 inches b 3 inches c 4 inches d 6 inches

Explanation:

Step1: Recall the formula for mechanical advantage (MA) of wheel - and - belt assembly

The formula for the mechanical advantage of a wheel - and - belt assembly is \(MA=\frac{\text{Diameter of driven wheel}}{\text{Diameter of driver wheel}}\). Let the diameter of the driver wheel be \(x\). We know that \(MA = \frac{1}{3}\) and the diameter of the driven wheel \(d_{driven}=12\) inches. So, \(\frac{1}{3}=\frac{12}{x}\).

Step2: Solve the equation for \(x\)

Cross - multiply the equation \(\frac{1}{3}=\frac{12}{x}\) to get \(x = 12\times3\div1\).

Answer:

C. 4 inches