# How high can it coast up the hill, if you neglect friction?

## Homework Statement

Suppose a 180 kg motorcycle is heading toward a hill at a speed of 29 m/s. The two wheels weigh 12 kg each and are each annular rings with an inner radius of 0.280 m and an outer radius of 0.330 m.
How high can it coast up the hill, if you neglect friction in m?

*m = 180 kg
*v = 29 m/s
*h = 32 m

2. Homework Equations

mgh = 1/2 m v^2 + 1/2 I w^2

## The Attempt at a Solution

First thing I did is finding the moment of inertia for the wheels, which is 1/2 m (b^2 + a^2) then I multiplied it by 2 since there are two wheels.

I then plugged that number for "I" in the above equation. I found w by dividing the given velocity by the outer radius(not sure if that is right) and then I had all the variables and solved for h but got an unreasonable number! bigger that the actual height of the hill.

## Answers and Replies

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haruspex
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I then plugged that number for "I" in the above equation. I found w by dividing the given velocity by the outer radius(not sure if that is right) and then I had all the variables and solved for h but got an unreasonable number! bigger that the actual height of the hill.
It's hard to be sure without seeing all your working, but it sounds like you only considered the wheels getting up the hill. Even then, I don't think you should have got an unreasonable answer. If you do not show you working we cannot tell where you went wrong.

• CWatters