http://i.imgur.com/DVNEJPx.png need help with A and B, the stuff below is just r

Question

http://i.imgur.com/DVNEJPx.png

need help with A and B, the stuff below is just reference.

Recall the situation from the prelab involving Apparatus 1 and Apparatus 2. Suppose now that block 1 is replaced with a new block that has twice the mass as the original (i.e., 2m compared to m). It is found that in this new situation the blocks hit the floor at the same tune. In this new situation, while the blocks are falling: Is the acceleration of the block in Apparatus 1 greater than, less than, or equal to the acceleration of the block in Apparatus 2? Explain. is the tension in the string in Apparatus 1 greater than, less than, or equal to the tension in the string in Apparatus 2? Explain. What can be said about the ratio of the moment of inertia of the wheel to that of the disk (i.e., I1/12)? Explain. Find a numerical value if possible. Consider Apparatus 1 and Apparatus 2 shown at right. In each case: a block of mass m is attached to one end of a light string; the string is wound up on the outside rim of a wheel; and the wheel is free to rotate about a fixed pivot. The only difference is that in Apparatus 1, the wheel is a metal rim with spokes, while in Apparatus 2, it is a solid disk. (The spoked wheel and the solid disk have the same mass M and the same radius R.)

Explanation / Answer

a) since they hit the ground at the same time the acceleration is the same

Now for tensions

mg - T = ma

so t = mg -ma

so more mass means more T

so 1 is less than 2


b)

so we know for 1

mg - T = ma

and r T = I1 alpha

T = I1 a/r^2

add

so

mg - I1 a/r^2 = ma

I1 = m ( g-a) r^2/a

so for 2:
I2 = 2 m(g-a) r^2/a

so I1/I2 = 1/2

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