To practice Problem-Solving Strategy 8.1 Static equilibrium problems. When you l

Question

To practice Problem-Solving Strategy 8.1 Static equilibrium problems.

When you lift an object by moving only your forearm, the main lifting muscle in your arm is the biceps. Suppose the mass of a forearm is 1.30 ({ m kg}) . If the biceps is connected to the forearm a distance ( exttip{d_{ m biceps}}{d_biceps}) = 2.50 ({ m cm}) from the elbow, how much force ( exttip{F_{ m biceps}}{F_biceps})must the biceps exert to hold a 1000 ({ m g}) ball at the end of the forearm at distance ( exttip{d_{ m ball}}{d_ball}) = 35.0 ({ m cm}) from the elbow, with the forearm parallel to the floor? How much force ( exttip{F_{ m elbow}}{F_elbow}) must the elbow exert?(Figure 1)

What is the horizontal distance dforearmbetween the elbow and the point where the weight of the forearm acts?

Explanation / Answer

i) Sum the moments about the elbow:
1.0kg * 9.8m/s² * 35cm + 1.3kg * 9.8m/s² * 35cm/2 = Fbiceps * 2.5 cm
Fbiceps = 226.38N

(Given no other information, "the horizontal distance d of forearm between the elbow and the point where the weight of the forearm acts" is d = L/2 = 35cm / 2 = 17.5 cm.)

ii) Sum the vertical forces:
(1.0 + 1.3)kg * 9.8m/s² + Felbow = Fbiceps
22.54N + Felbow = Fbiceps
Felbow = 203.84N

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