Question

The drawing shows a model for the motion of the human forearm in throwing a dart. Because of the force 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 0.065 kg . m2 (including the effect of the dart) relative to the axis at the elbow. Assume also that the force M acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force M needed to give the dart a tangential speed of 5.0 m/s in 0.10 s. starting from rest.

Answer 1

464.3 N

Step-by-step explanation:

Given parameters are:

I = 0.065
`kg*m^2`

L = 0.025 m

R = 0.28 m

`v_0` = 0 m/s

`v_f` = 5 m/s

t = 0.1 s

`v_f=v_0+at=at`

Hence,
`a=v_f/t`

We must connect two torque equations to find the answer.

`\tau=LM=I\alpha`

Where
`\alpha =(a)/(R) =(v_f)/(Rt)`

Hence,
`LM=I(v_f)/(Rt)`

Thus,
`M = (Iv_f)/(LRt) = (0.065*5)/(0.025*0.28*0.1) =464.3` N