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

Question

The figure shows a model for the motion of the human forearm in throwing a dart. Because of the force  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 figure and a moment of inertia of 0.059 kgm2 (including the effect of the dart) relative to the axis at the elbow. Assume also that the force  acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force  needed to give the dart a tangential speed of 5.4 m/s in 0.14 s, starting from rest.

Explanation / Answer

The angular velocity ? needed is v/r = 5.4m/s/0.28m = 19.285 rad/s

To achieve this speed in 0.14s requires an angular acceleration ?

? = ?/t = 19.285/0.14 = 137.755 rad/s^2

Now torque = F*d = I*?

So F = I*?/d = 0.059*137.755/0.28 = 29.027N

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