Posted by **Morgan** on Saturday, November 5, 2011 at 2:09am.

15. [1pt] A thin hoop of radius r = 0.59 m and mass M = 9.2 kg rolls without slipping across a horizontal floor with a velocity v = 3.3 m/s. It then rolls up an incline with an angle of inclination θ = 31°. What is the maximum height h reached by the hoop before rolling back down the incline?

- Physics -
**drwls**, Saturday, November 5, 2011 at 6:03am
The initial kinetic energy before it starts climbing is

KEmax = (1/2)MV^2 + (1/2)I*w^2

where I = M R^2 and w = V/R.

I is the moment of intertia, R is the radius, V is the initial velocity and and w is the initial angular velocity.

Combining terms,

KEmax = M V^2.

It stops rolling when

KEmax = M g h,

the potential energy increase.

h = V^2/g. The ramp angle, hoop mass and radius do not matter.

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