# Pendulum Physics

1. May 8, 2012

### sawtooth500

You have a pendulum with a 100 ft radius and 200 lb weight. The weight is dropped at the same height as the anchor point 100 ft away from anchor. How do I calculate the tension that will exist on the line?

Also, are there any other forces involved here? I need to calculate this to make sure I have a sufficiently strong line so that it does not snap.

2. May 8, 2012

### tiny-tim

hi sawtooth500!
write out F = ma in the direction of the line (the only forces are the weight and the tension) …

what do you get?

3. May 8, 2012

### fictionx

T=F=ma only in the most downward position. Otherwise the tension is a function of the angle. You must calculate the component of the weight of the load perpendicular to its path as a function of the angle.

4. May 8, 2012

### sawtooth500

So basically the tension in the line is never going to exceed the weight of the pendulum, and you'd be at max tension when the pendulum is straight vertical down, correct?

5. May 8, 2012

### tiny-tim

no, you're forgetting the centripetal acceleration

write out F = ma in the direction of the line (the only forces are the weight and the tension) …

what do you get?

6. May 8, 2012

### sawtooth500

So you got 200 lbs of mass, 200 * 32.2 = 6440 lbs of force?

7. May 13, 2012

### the_emi_guy

Max tension will be at the bottom of the swing and will consist of both mg (pulling against gravity) and the centripetal force (keeping pendulum swinging in circular path).
Here is the procedure:
Use conservation of energy to find velocity of pendulum at bottom of the swing: mgh = (1/2)mv^2.
From velocity, find centripetal force at bottom of swing = (mv^2)/r
So tension = mg + (mv^2)/r

By the way if this 200 pound pendulum is a human body you better in include a safety factor.

8. May 13, 2012

### sawtooth500

Yeah basically it is a gonna be a human body - rope is rather to 5000 lbs of tension, I thought it should be enough but I just wanted to be sure...

9. May 14, 2012

### jehan60188

if you can't figure a problem like this out on your own, you probably shouldn't be doing anything that involves the safety of human beings.