# Pendulum with mass attached.

1. Apr 19, 2013

### SherlockOhms

1. The problem statement, all variables and given/known data
A pendulum of mass "m" reaches a height "h" , while the length of the pendulum is R. If the R = 262 cm and h = 136 cm: (a) calculate the max speed in the x-direction.
(b) calculate the max speed in the y direction.

2. Relevant equations
K = 1/2(m)(v)^2.
U = mgh.
Vector components.

3. The attempt at a solution
Calculating the max speed in the x direction is grand, it obtains a maximum value at the bottom of the arc so using conservation of energy you can calculate it to be v = sqrt(2gh). This is due to the vector components of the pendulum's velocity being v = vcos(θ)x + vsin(θ)y. The x-component obtains a max value when cos(θ) = 1 which occurs at θ = 0 (i.e. the bottom of the arc). Wouldn't the y-component then obtain a max value when θ = pi/2? This angle is never actually reached due to the bob only being raised through a height "h".
So calculating the max velocity in the y is a little trickier. Could somebody give me some advice on what to do next? I'll attach a picture of the diagram.

2. Apr 19, 2013

### SherlockOhms

3. Apr 19, 2013

### vela

Staff Emeritus
You should be able to write down an expression for the potential energy of the mass as a function of $\theta$. Using it, you can derive an expression for v as a function of $\theta$.

4. Apr 19, 2013

### SherlockOhms

I'm not given θ though. Is there enough information given to find it?

5. Apr 19, 2013

### vela

Staff Emeritus
$\theta$ is a variable that tells you where the pendulum is. It changes with time. Did you mean $\theta_0$, the initial value of $\theta$? You are, in fact, given enough information to find it, but I'm not sure why you'd need it.

6. Apr 19, 2013

### SherlockOhms

Ok, ok. I see what you're saying now. Misunderstood your first reply. Thanks!