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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.

Respuesta :

erturkmemmedli

Answer:

464.3 N

Explanation:

Given parameters are:

I = 0.065 [tex]kg*m^2[/tex]

L = 0.025 m

R = 0.28 m

[tex]v_0[/tex] = 0 m/s

[tex]v_f[/tex] = 5 m/s

t = 0.1 s

[tex]v_f=v_0+at=at[/tex]

Hence, [tex]a=v_f/t[/tex]

We must connect two torque equations to find the answer.

[tex]\tau=LM=I\alpha[/tex]

Where [tex]\alpha =\frac{a}{R} =\frac{v_f}{Rt}[/tex]

Hence, [tex]LM=I\frac{v_f}{Rt}[/tex]

Thus, [tex]M = \frac{Iv_f}{LRt} = \frac{0.065*5}{0.025*0.28*0.1} =464.3[/tex] N

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