A- what force does the biceps muscle exert on the forearm? A 70.5 kg weight lift

Question

A- what force does the biceps muscle exert on the forearm?
A 70.5 kg weight lifter is doing arm raises using a 7.50 kg weight in her hand. Her arm pivots around the elbow joint, starting 40.0° below the horizontal. (See the figure (Figure 1) ) Biometric measurements have shown that both forearms and the hands together account for 6.35 % of a person's weight. Since the upper arm is held vertically, the biceps muscle always acts vertically and is attached to the bones of the forearm 5.50 cm from the elbow joint. The center of mass of this person's forearm- hand combination is 19.0 cm from the elbow joint, along the bones of the forearm, and the weight is held 38.0 cm from the elbow joint. Figure 1 Y Figure 1 of 1 Biceps muscle Joint 40.0

Explanation / Answer

mass of the fore arm = m1 = (1/2)*0.0635*70.5 = 2.24 kg

r1 = 19 cm = 0.19 m

mass of the weight m2 = 7.5 kg

r2 = 38 cm = 0.38 m

net torque about the elbow = 0

m1*g*r1*cos40 + m2*g*r2*cos40 - F*r3*cos40 = 0

F*r3 = m1*g*r1*cos40 + m2*g*r2*cos40

F*0.055*cos40 = (2.24*9.8*0.19*cos40)+(7.5*9.8*0.38*cos40)

F = 583.6 N

along vertical net force = 0

Fy + F - (m1+m2)*g = 0

Fy +583.6 - (2.24+7.5)*9.8 = 0

Fy = -488.15 N

the magnitude of the force that the elbow joint exerts on the forearm = 488.15 N (down wards)

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