*40.   Multiple-Concept Example 10 reviews the approach and some of the concepts that are pertinent to this problem. The drawing 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 drawing and a moment of inertia of 0.065 kg × 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 5.0 m/s in 0.10 s, starting from rest.

 

w0439

 

Where L = 0.025 m is the lever arm the muscle force M is acting on.

 

I is the moment of inertia given in the problem as 0.065 kg m2

 

Where R = 0.28 m is the radius which the tangential acceleration a is acting.

We know:

use

Solve for a

So putting this all together

So solving for M

 

 

 

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This page last updated on January 11, 2020