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**1. Homework Statement :**

A rock of mass m is attached to a string of negligible mass and length L. The rock is released from rest from a horizontal position. When the rock is at point P, the string attached to the rock makes an angle θ with the horizontal.

In terms of the quantities, m, L, θ and any necessary constants:

a. Draw a free-body diagram of the rock at point P.

b. Find the speed of the rock at point P.

c. Find the tension in the string at point P.

d. Find the tangential acceleration of the rock at point P.

## Homework Equations

Newton's Laws

Energy equations

Tangential Acceleration = (angular velocity/time)

## The Attempt at a Solution

I originally tried using only newton's laws to solve this (I went through and solved the entire problem), only to realize that it was not in the correct quantities (m, L, θ).

I thought of re-doing this problem using energy, but I'm not entirely sure how to go about doing that. I also figured that if I DID use energy to solve this, I would be lacking a time variable which I would have needed in part D.

Putting up my work here seems pointless since it's wrong, but I'll give a general outline of what I did:

1) Drew FBD of rock at point P.

2) Found the velocity in the X and Y directions using F

_{net}= mv^2/r and used the Pythagorean theorem to find the speed (this had a tension term in it, which should not be a part of the answer...).

3) Rewrote the expression I got for velocity in terms of tension to find the tension (this had velocity in it, which should not be a part of the answer...).

4) Found tangential acceleration using w/t, where w = the velocity I solved for earlier, and t=t (t should not be a part of the answer...).

I'd appreciate if someone could give an outline similar to the one above of what I should have done to solve this problem correctly with the correct quantities (m, L, θ). Please include the equation and concept that I should use (this is more or less for understanding mainly), as well a general idea of what I should end up with.

Diagram and Free-Body Diagram:

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