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%.

Questions: Calculate ideal mechanical advantage when the effort force is applied to the axle.

Questions: considering the efficiency calculate the actual mechanical advantage of the wheel and axle.

Questions: If you used the same wheel and axle in a different way and applied effort force to the wheel to drive the axle, what is the ideal mechanical advantage of the wheel and axle?

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AFOKE88go AFOKE88go · Answer 1

The answer for the ideal mechanical advantage and actual mechanical advantage for the different scenarios are;

A) Ideal Mechanical Advantage = 18.67

B) Actual Mechanical Advantage = 4.1067

We are given;

Input distance; The diameter of the wheel; d_w = 14 inches

Output distance; The diameter of the axle that drives the wheel; d_a = 3/4 inches

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

The efficiency of the band saw; η = 22% = 0.22

A) Formula for Mechanical advantage is;

M.A = Force output/Force input = (Input distance)/(Output distance)

Thus;

Ideal mechanical advantage = 14/(3/4)

Ideal mechanical advantage = 18.67

B) Now, we are given that efficiency of the band saw is η = 22% = 0.22.

Thus using the mechanical advantage formula above;

Actual mechanical advantage = 0.22 × Expected output

Actual mechanical advantage = 0.22 × 18.67

Actual mechanical advantage ≈ 4.1067

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