# Pendulum Problem

1. Apr 3, 2008

### Dgolverk

1. The problem statement, all variables and given/known data
Calculate the maximum speed of 100g pendulum mass when it has a length of 100cm and an amplitude of 50cm.

2. Relevant equations
I think that Eg=mgh and Ek=0.5mv^2 are related to this problem.

3. The attempt at a solution
I'm not really sure how to start this problem as I don't know how to calculate the height for Eg. However I'm pretty sure that I need to use further on gh=0.5v^2 as mass cancels in this situation. Sorry that I cannot provide a full attempt, but I just don't understand part of the problem.
I just tried to solve it again and that what I got:
sqrt(g/L)
=sqrt(9.8/1)
=3.13

v(max)=(.5)(3.13)
=1.57 m/s
Anything right?

Last edited: Apr 3, 2008
2. Apr 4, 2008

### physixguru

HINT:
The speed of a simple pendulum is maximum at its center.
Also ..

v= -A * omega *cos(omega*t + phase angle ) [S.H.M. EQUATION]

At center phase angle equals zero.

Last edited: Apr 4, 2008
3. Apr 4, 2008

### Staff: Mentor

Measure heights from the lowest point. Figure out the initial height of the mass by first figuring out its vertical distance from the support point: Consider the triangle whose hypotenuse is the length of the pendulum and whose base is the amplitude.

Draw a diagram!
That's what you need.

4. Apr 4, 2008

### Dgolverk

So by I found out the vertical distance from the support point is 86.6cm, however it does not make sense, if the length is 100cm wouldn't the height at rest be the same?
I can continue from here but I need explanation about the height.
Thank you again

5. Apr 4, 2008

### Staff: Mentor

Initially the mass is 86.6 cm below the support point. So how high is it above the lowest point? (How high is the support point?)

6. Apr 4, 2008

### Dgolverk

I'm really sorry but I'm a bit confused about the wording, if the lowest point is 86.6cm then I just subtract this from 100cm therefore the height of the mass before it is released is 13.6cm? I just can't figure it out. Can you please give me a hint or some further explanation.
Thank you for you patience.

Last edited: Apr 4, 2008
7. Apr 4, 2008

### Staff: Mentor

Exactly!

If you are having a hard time visualizing this, draw a diagram showing the pendulum at its highest and lowest point.

Note: The highest position of the mass is 86.6cm below the support, which means it is 13.4cm above the reference point.

Last edited: Apr 4, 2008
8. Apr 4, 2008

### Dgolverk

Alright! :D
So now I need to calculate Eg at h=13.6cm Ek=0 before released.
But how do I calculate the speed at the bottom?

9. Apr 4, 2008

### Staff: Mentor

Use conservation of energy. You already gave the correct formula.

10. Apr 4, 2008

### Dgolverk

Therefore Ek at the bottom will equal the same as Eg before release.
Ek = 0.5mv^2
Then I need to find v?

Last edited: Apr 4, 2008
11. Apr 4, 2008

### Staff: Mentor

Exactly.

Mechanical energy is conserved, so Ek(1) + Eg(1) = Ek(2) + Eg(2). Since we measure Eg from the bottom level, Eg(2) = 0; that gives you:
Eg(1) = Ek(2)
mgh = 0.5mv^2

12. Apr 4, 2008

### Dgolverk

Thank you very much!

13. May 23, 2008

### mr.worm

doc could you help me out here
I am stumped... I just sent you a report on what data I have collected this far

14. May 23, 2008

### mr.worm

nope, got it now. But another note. How do I find the Acc. due to grav.???

15. May 24, 2008

### Staff: Mentor

How does the period of a pendulum depend on its length and the acceleration due to gravity?