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 0.064 kg middot m2 (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 4.8 m/s in 0.11 s, starting from rest.

Explanation / Answer

From kinematics the acceleration needed to accelerate an object from 0 to 5m/s in 0.10s
a = 4.8/.11 = 43.63 m/s^2 This corresponds to an angular acceleration

alpha = a/r = 43.63/.28 = 155.82 RAD/S^2



Now use torques = I*alpha

The torque is M*0.022 = 0.064*155.82

So M = 0.064*155.82/0.022 = 453.3 N

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