# Couple mechanics problems

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 = $$\frac{1}{2}$$m$$v^2$$ + $$\frac{1}{2}$$I$$\omega^2$$+ $$\frac{1}{2}$$k$$x^2$$

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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## Answers and Replies

OlderDan
Science Advisor
Homework Helper
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 = $$\frac{1}{2}$$m$$v^2$$ + $$\frac{1}{2}$$I$$\omega^2$$+ $$\frac{1}{2}$$k$$x^2$$

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, $\omega$ is proportional to v. Combine the first two terms to get something that looks like $\frac{1}{2}Mv^2$
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