(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A large hoop rolls without slipping across a horizontal surface. The hoop has a constant translational speed of 9.2 m/s, a mass m of 16 kg, and a radius r of 1.3 m. The moment of inertia of the hoop about its center of mass is 1mr^2. The hoop approaches a 22° incline of height 4 meters and rolls up the incline without slipping.

All parts of the problem up to this point are shown below under "Relevant Equations"

f) You lift it beyond the maximum angle, so when the hoop hits the ramp, it climbs but it does slip. Does the hoop go to a higher altitude than it did in part a?

2. Relevant equations

a) calculate the total kinetic energy of the hoop as it rolls along the horizontal surface.

Found to be 1354.24 J

b) i) Calculate the magnitude of the velocity of the hoop just as it leaves the top of the incline.

Found to be 6.74 m/s

ii. Specify the direction of the velocity of the hoop just as it leaves the top of the incline.

Found to be 22 degrees

c) Neglecting air resistance, calculate the horizontal distance from the point where the hoop leaves the incline to the point where the sphere strikes the level surface.

Found to be 7.48 m

d) Calculate the force of friction (while its on the ramp) and its direction (up the ramp being positive, down the ramp being negative)

Found to be 29.38 N

e) You increase the angle of the ramp to see if the hoop will go farther. What is the MAXIMUM angle of the ramp (above horizontal) you can increase it to without the hoop slipping, if the ramp has coefficient of static friction = 0.42.

Found to be 40.03 degrees

3. The attempt at a solution

I believe the answer would be no, it does not reach a higher altitude because once you exceed the angle found in part (e), the static friction is overcome by the rotational velocity (omega) of the hoop, which allows the hoop to spin faster. This would therefor increase the rotational kinetic energy of the hoop, allowing less for translational kinetic energy and thus less translational velocity so the hoop would not get as high.

I'm just looking for a confirmation of whether or not I am correct, and an explanation if I am incorrect as this is a crucial question on my homework assignment.

Thanks,

CornDog

EDIT - This assignment is due about 1 day from right now, so quick responses would be appreciated.

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# Hoop Rolling Up Ramp

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