# Homework Help: Very Simple Work/Energy Pendulum Problem

1. Jan 15, 2012

1. The problem statement, all variables and given/known data
A 2.0kg bob of a pendulum is held at an angle of 55 degrees from the vertical. When released it reaches a maximum speed of 3.5m/s. What is the length of the pendulum arm?

2. Relevant equations
Ek = 1/2mv^2
Ep = mgh

3. The attempt at a solution

1/2 * 2 * 3.5 ^ 2 = 12.25 J
12.25 = 2(9.8)h
h = 0.625

That's as far as I can get. I know that the length of the pendulum arm is 0.625 plus "length - 0.625" but I'm stuck there. Help would be much appreciated :)

2. Jan 15, 2012

### Simon Bridge

Draw the picture - h is the vertical distance between the start position and the bottom of the arc - and you know the angle of the arc is 55 degrees.

Construct the obvious triangle and use trig.

3. Jan 15, 2012

Could you please specify what the triangle would look like and which trig functions to use? I know that h is the vertical distance between the start position and the bottom of the arc and that I should use trig on a constructed triangle but I'm a little brain dead as of now and totally stonewalled.

4. Jan 15, 2012

### Simon Bridge

Did you draw the picture?
There's only like, two possible triangles.

Hint: you want the one where the third side is horizontal.
Draw it and stare at it - keep staring at it: what is the length of the hypotenuse? What is the length of the vertical side? How are these related?

5. Jan 15, 2012

I did draw the picture; there's a big triangle of which the three sides are the vertical, the string, and an imaginary horizontal line, and a small one of which the three sides are h, the imaginary horizontal, and a hypotenuse roughly where the pendulum bob would swing. I've been staring at it for a good half hour before making a topic... maybe my algebra or trig is rusty? Sorry Simon, I'm not seeing anything.

6. Jan 15, 2012

### Simon Bridge

You will kick yourself...

Write the expression for the cosine of 55 using this triangle, and solve for r.

#### Attached Files:

• ###### pend1.png
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7. Jan 15, 2012

Thanks for the diagram! That's what I had down, and I tried to use sine law but I can only get to sin35 = (r - 0.625) / r

I hate having people spell things out for me but I am just not getting this :(

8. Jan 15, 2012

### Simon Bridge

That should do it! You just used the complimentary angle.
I was suggesting you do:$$\cos(55)=\frac{r-h}{r}$$(remember SOH CAH TOA?)
But yours is exactly the same.

Now solve for r.

You can do algebra right?
This is an equation of the form: ax = x - b