Couple mechanics problems

  • Thread starter blackbody
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Hi, I have a couple general (pretty much abstract) mechanics questions, and I'm not sure I'm going the right way about doing them. Any help would be appreciated.

1)On a flat surface with friction, you have a massless spring with a spring constant (k) attached to a wall on one end, and on the other end to a solid cylinder of radius R, which can roll back and forth, due to oscillation. How can you find the time for one period/oscillation?

Ok, so the total mechanical energy is the sum of the kinetic (translational and rotational) and potential energies:
E = [tex]\frac{1}{2}[/tex]m[tex]v^2[/tex] + [tex]\frac{1}{2}[/tex]I[tex]\omega^2[/tex]+ [tex]\frac{1}{2}[/tex]k[tex]x^2[/tex]

I don't know whether to consider this SHM...how would I go about doing this?

2) You have a dam with a certain height of water against it. The pressure of the water can be given as a function of the height of the water p(h). What is the total force acting on the dam?

I'm thinking you just integrate the pressure function from 0 to the height?
 
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OlderDan
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blackbody said:
Hi, I have a couple general (pretty much abstract) mechanics questions, and I'm not sure I'm going the right way about doing them. Any help would be appreciated.

1)On a flat surface with friction, you have a massless spring with a spring constant (k) attached to a wall on one end, and on the other end to a solid cylinder of radius R, which can roll back and forth, due to oscillation. How can you find the time for one period/oscillation?

Ok, so the total mechanical energy is the sum of the kinetic (translational and rotational) and potential energies:
E = [tex]\frac{1}{2}[/tex]m[tex]v^2[/tex] + [tex]\frac{1}{2}[/tex]I[tex]\omega^2[/tex]+ [tex]\frac{1}{2}[/tex]k[tex]x^2[/tex]

I don't know whether to consider this SHM...how would I go about doing this?

2) You have a dam with a certain height of water against it. The pressure of the water can be given as a function of the height of the water p(h). What is the total force acting on the dam?

I'm thinking you just integrate the pressure function from 0 to the height?
As long as you are rolling without slipping, [itex]\omega[/itex] is proportional to v. Combine the first two terms to get something that looks like [itex]\frac{1}{2}Mv^2[/itex]
where M is a constant that is made up of the mass and moment of inertia. You should be able to take it from there.

You have the right idea about the dam
 

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