A bicycle mechanic is checking a road bike's chain. He applies force F = 48 N to a pedal at the angle shown in (Figure 1) while keeping the wheel from rotating. The pedal is 17 cm from the center of the crank; the gear has a diameter of 16 cm.

T = 102.3 ≈ 100

Explanation:

r(pedal) = 17 cm = 0.017 m

r(gear) = 16 cm / 2 = 8 cm = 0.008 m

θ = 180°-110° = 70°

F = 48 N

T = ?

τ₁ = r(pedal)*F*cosθ = (0.017 m)(48 N)cos(70°) = 0.28 N*m (*negative because it is applied clockwise)

τ₂ = -τ₁ = -(-0.28 N*m) = 0.28 N*m

τ₂ = r(gear)*T*cosθ

T = τ₂÷(r(gear)*cosθ) = 0.28 N*m ÷ (0.008 m * cos(70°))

T = 102.3 ≈ 100 ( 2 sig figs)

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explanation:

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