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**1. Homework Statement**

A cart is rolling down an incline (angle to horizontal is theta). It has two wheels, each wheel has mass m and moment of inertia mR^2/2. The total mass of the cart and the two wheels is M. Using conservation of energy (assuming no friction between cart and axles), show that the acceleration of the cart along the incline is a = [M/(M + 2m)] g sin theta.

**2. Homework Equations**

K = Iw^2/2

K = mv^2/2

v = wR (w is angular velocity).

v^2 = 2as

**3. The Attempt at a Solution**

E0 = E1

Ug = 2(K_rolling) + K_trans

Letting d be the distance traveled on the incline, this gives:

Mgd sin(theta) = (Iw^2/2)2 + Mv^2/2 = Iw^2 + Mv^2/2

Using the given moment of inertia I = mR^2/2:

Mgd sin(theta) = (mR^2/2)w^2 + Mv^2/2

Mgd sin(theta) = mv^2/2 + Mv^2/2

v^2 = 2Mgd sin(theta)/(M + m)

v^2 = 2ad:

a = Mg sin(theta)/(M + m)

:surprised

I can't figure out where they got the 2m from.

I've tried adjusting the height by the radius of the wheels, but that gets complicated, because there are two of them, at two different heights, and I can't believe that would lead to the formula they give.

When you all recover from New Years, I'd appreciate any suggestions

Dorothy

(This is from Serway and Jewett, btw, 10.89)

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