Analyze the example of this band saw wheel and axle. The diameter of the wheel is 14 inches. The diameter of the axle that drives the wheel is 3/4 inch. The actual force needed to cut through a one-inch-thick softwood board is 1.75 pounds. Consider the efficiency of this band saw to be 22%. Considering the efficiency of this system, calculate the actual mechanical advantage of the wheel and axle

The actual mechanical advantage of the wheel and axle is approximately 4.1067

Explanation:

The given parameters are;

The diameter of the wheel = 14 inches

The diameter of the axle that drives the wheel = 3/4 inches

The force needed to cut a one-inch-thick softwood board = 1.75 pounds

The efficiency of the band saw  = 22%

Mechanical advantage = Force output/Force input = Input distance/(Output distance)

Input distance/(Output distance) = 14/(3/4) ≈ 18.67

Mechanical advantage ≈ 18.67

Given that efficiency = Useful energy output/(Total energy input), we have;

Efficiency = 22% = 0.22 × Expected output, we have;

The actual mechanical advantage = 0.22 × 18.67 ≈ 4.1067

The actual mechanical advantage ≈ 4.1067