<p>Leg raises.A person of mass M lies on the floor doing leg raises. His leg is

Question

<p>Leg raises.A person of mass M lies on the floor doing leg raises. His leg is 0.90 m long and pivots at the hip. Treat his legs (including feet) as uniform cylinders, with both legs comprising 34.5% of body mass, and the rest of his body as a uniform cylinder comprising the rest of his mass. He raises both legs 60^o above the horizontal.</p>
<p>(a)How far does the center of mass of each leg rise?Express your answer to two significant figures and include the appropriate units.</p>
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<p>(b)How far does the entire body's center of mass rise?Express your answer to two significant figures and include the appropriate units.</p>

Explanation / Answer

The person's mass is M
the length of the leg is L = 0.9 m
The percent of mass of the two legs is 34.5%
The angle above the horizontal through which the legs are raised is theta = 60 degree

1)
The leg's center of mass is at the middle of the length of the leg.
so his leg center of mass is rise for h=0.9 m * 0.5 * sin(60) = 0.39 m.
2)
In the y component,
let the height of the entire body's center of mass be H.
H*M = 0*0.655*M + 0.39*0.345*M.
so H=0.13 m

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