A woman tosses a 1.00 kg soft drink bottle vertically upward to a friend on a ba

Question

A woman tosses a 1.00 kg soft drink bottle vertically upward to a friend on a balcony above. At the beginning of the toss, her forearm rotates upward from the horizontal so that her hand exerts a 25 N upward force on the bottle. Determine the force that her biceps exert on her forearm during this initial instant of the throw. The mass of her forearm is 1.5 kg and its rotational inertia about the elbow joint is 0.065 kg m2. The attachment point of the biceps muscle is 4.0 from the elbow joint, the hand is 30 cm away from the elbow, and the center of the mass of the forearm/hand is 15 cm from the elbow.

Explanation / Answer

Here,

m = 1 Kg

F = 25 N

m1 = 1.5 Kg

I = 0.065 Kg.m^2

acceleratio , a = (25 - 10)/(1) = 15 m/s^2

angular acceleration = 15/0.30 = 50 rad/s^2

let the biceps force is F

Balancing the torque about the joint

(0.065 + 1 * 0.30^2) * 50 = F * 0.04 - 1 * 10 * 0.30 - 0.15 * 1.5 * 10

solving for F

F = 325 N

the force exerted by the biceps muscle is 325 N

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