The drawing shows a model for the motion of the human forearm in throwing a dart

Question

The drawing shows a model for the motion of the human forearm in throwing a dart. Because of the force vector M applied by the triceps muscle, the forearm can rotate about an axis at the elbow joint. Assume that the forearm has the dimensions shown in the drawing and a moment of inertia of 0.057 kg · m2 (including the effect of the dart) relative to the axis at the elbow. Assume also that the force vector M acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force vector M needed to give the dart a tangential speed of 4.7 m/s in 0.11 s, starting from rest.

Explanation / Answer

From kinematics the acceleration needed to accelerate an object from 0 to 4.7 m/s in 0.11s

a = 4.7/0.11 = 42.73 m/s^2

angular acceleration alpha = a/r = 42.73/0.28 = 152.61 rad/s^2

Now use torques = I*alpha

The torque is M*0.025 = 0.057*152.62

M = 347.9 N

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