We analyzed the biceps muscle example with the angle between

We analyzed the biceps muscle example with the angle between forearm and upper arm set at 90°. Find the force exerted by the biceps muscle when the angle is 130° and the forearm is in a downward position. (Assume that

r₁ = 6.0 cm,

r₂ = 14 cm,

r₃ = 32 cm,

m_a = 2.0 kg,

and

m_b = 4.8 kg.

Enter the magnitude.)

Solution

the net torque is zero when the system is in equailibrium:

Tnet = 0

(F_E x 0) + (F_B x r₁) + (W_a x r₂) + (W_a x r₃) =0

then,

(F_B x r₁) = (W_a x r₂) + (W_a x r₃)

(F_B r₁sin40) = (W_ar₂sin40) + (W_br₃sin40)

(F_B *0.06*sin40) = (2.0*9.8*0.14*sin40) + (4.8*9.8*0.32*sin40)

therefore, the required force:

F_B= 296.6 N