# Pendulum Velocity

1. Sep 30, 2014

### Yae Miteo

1. The problem statement, all variables and given/known data
A mass m = 5.5 kg hangs on the end of a massless rope L = 1.81 m long. The pendulum is held horizontal and released from rest. How fast is the mass moving at the bottom of its path?

2. Relevant equations

$$a_c = \frac {v^2}{r}$$

$$F = ma$$

$$v = v_o + at$$

3. The attempt at a solution

I attempted to solve the problem by coming up with a formula, and then plugging in the numbers. To begin,

$$F = ma = m \frac {v^2}{r}$$

$$v = v_o + at = 0 + t \frac {v^2} {r}$$

so more neatly

$$F = m \frac {v^2}{r}$$

$$v = t \frac {v^2} {r}$$

but from here I'm stuck. I'm not sure how to find time, or even if it needs to be found at all. Any suggestions?

2. Sep 30, 2014

### cwasdqwe

Think of the conservation of energy:

what kind of energy does the mass have initially?
In which another kind of energy is then transformed into, once you drop the mass and let it swing?

3. Sep 30, 2014

### nasu

Before jumping to formulas, think what kind of motion is this. Is this accelerated motion? Is the acceleration constant?
Then you can decide what formula will apply to it.

4. Sep 30, 2014

### Yae Miteo

The initial energy will all be potential (PE = mgh) and the final energy will be entirely kintic (KE = 1/2 mv^2)

5. Oct 1, 2014

### Satvik Pandey

Yes .By equating PE and KE can you find v?

6. Oct 1, 2014

### cwasdqwe

You're right, Yae Miteo. And you have all the data to compute those numbers and find v. ;)