# Who Will Win In a Downhill Race?

**1. The problem statement, all variables and given/known data**

Out of these various shapes: a wooden disk, a modified wooden disk with four pieces of metal in the middle, a smaller metal disk, a metal hoop, a small metal sphere, and a cart with four small wheels, who will win in a race rolling down a ramp with height h and angle Θ? An image of the cart is attached.

**2. Relevant equations**

**v =** [itex]\sqrt{\frac{2gh}{1+c}}[/itex], **where c = coefficient of inertia**

**3. The attempt at a solution**

We did an experiment in class where we were given the various shapes listed above (excluding the cart), and using the equation above, I found that the modified disk would win the race by thinking that the coefficient of its inertia must be smaller than that of the sphere (which came in second place with a coefficient of inertia of 2/5). However, I am stuck on this problem now with the inclusion of the cart. Any help is appreciated.

http://ift.tt/1lfmXf3

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