# Rolling hoop across floor and up an incline

#### melissa_y

1) A thin hoop of radius r = 0.13 m and mass M = 8.1 kg rolls without slipping across a horizontal floor with a velocity v = 4.0 m/s. It then rolls up an incline with an angle of inclination theta = 33o. What is the maximum height h reached by the hoop before rolling back down the incline?

2) A uniform horizontal bar of length L = 5 m and weight 233 N is pinned to a vertical wall and supported by a thin wire that makes an angle of theta = 43o with the horizontal. A mass M, with a weight of 384 N, can be moved anywhere along the bar. The wire can withstand a maximum tension of 547 N. What is the maximum possible distance from the wall at which mass M can be placed before the wire breaks?

*I'm sorry I am asking all these questions, i just really don't even know where to begin and I've never had this much trouble with homework before. Please help me!

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#### wisredz

For the second question, first draw a picture depicting the problem. The centre of mass of the bar would be it's middle right? Now you can wind the tension of the bar itself... Sin43.T.5=233.5/2 Now suppose that the maximum possible distance you can put the ball on the bar is x meters. Now, x.384+233.5/2=T.5 . I don't the name of what I'm doing in English, but it is the force of rotating.

There shouldn't be any problem now.

As to your first question try to use kinetic and potantial energies of the mass...

#### wisredz

I can't seem to edit my post. I have done a mistake in my solution. You don't need to find T. The question says that the wire can support a maximum force of 547 N. Okay, we are interested in this moment. At this moment the rotation force of the wire is going to be, 547.sin43.5. And this shoud be equal to the sum of rotating forces of the ball and the weight of the bar itself.

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