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Most of the motion generated by joints in the human body are examples of levers. An example of a third class lever is the forearm; the force which generates the motion is located in‑between the pivot point and the resistance force. The elbow acts as the pivot point, the biceps muscle pulls up on the forearm to move the mass which is held in the hand. Imagine someone is holding an object in her hand with her forearm horizontal and her upper arm vertical so her elbow creates a 90 ∘ angle. If her biceps attach to her forearm 0.0425 m from the elbow and make an angle of 30.0 ∘ with the vertical while a 3.14 kg mass is held in her hand 30.75 cm from the elbow, what force F is exerted by the biceps muscle? Ignore the mass of the forearm.

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Answer:

257.48055 N

Explanation:

m = Mass of object = 3.14 kg

s = Distance her biceps attach to her forearm from the elbow = 0.0425 m

[tex]\theta[/tex] = Angle = 30°

h = Elbow to arm distance = 30.75 cm

g = Acceleration due to gravity = 9.81 m/s²

The net torque which would be acting on the object about a vertical axis passing through the elbow is zero. So, we have the following relation

[tex]mgh=Fscos\theta\\\Rightarrow F=\frac{mgh}{scos\theta}\\\Rightarrow F=\frac{3.14\times 9.81\times 0.3075}{0.0425\times cos30}\\\Rightarrow F=257.48055\ N[/tex]

The force exerted by the biceps muscle is 257.48055 N

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