A 70 kg man's arm, including the hand, can be modeled as a 75 cm long uniform cylinder with a mass of 3.5 kg. In raising his both his arms, from hanging down to straight up, by how much does he raise his center of gravity?
**Looks like we're using 7 kg as both arms, calling his body's center of gravity to the ground as h1 and the center of gravity of the arm to the ground (before raising it) as h2. So when he raises his arms the new distance from the center of gravity to the ground is 7kg (h2 + 0.75) Then we're multiplying it out to get 7h2 + 5.25 ... but then we divide by something??
Or if you can figure it out using different methods, anything would help!!! Thanks!!!
**Looks like we're using 7 kg as both arms, calling his body's center of gravity to the ground as h1 and the center of gravity of the arm to the ground (before raising it) as h2. So when he raises his arms the new distance from the center of gravity to the ground is 7kg (h2 + 0.75) Then we're multiplying it out to get 7h2 + 5.25 ... but then we divide by something??
Or if you can figure it out using different methods, anything would help!!! Thanks!!!
-
You pretty much have it. You have to multiply the various heights by the appropriate mass and divide by the total.
Let "M" be the total mass and "2m" be the mass of the two arms.
Then initially the CM is;
Xi = [(M-2m)h1 + (2m)h2]/M
And finally;
Xf = [(M-2m)h1 + (2m)(h2 + .75)]/M
Subtract;
Xf - Xi = (2m)(.75)/M
Let "M" be the total mass and "2m" be the mass of the two arms.
Then initially the CM is;
Xi = [(M-2m)h1 + (2m)h2]/M
And finally;
Xf = [(M-2m)h1 + (2m)(h2 + .75)]/M
Subtract;
Xf - Xi = (2m)(.75)/M