Calculating Pendulum Tension with 100ft Radius & 200lb Weight

[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.

 

[tiny-tim]

hi sawtooth500!

How do I calculate the tension that will exist on the line?

Also, are there any other forces involved here?

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

what do you get? ​

 

[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.

 

[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?

 

[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? ​

 

[sawtooth500]

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

 

[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.

 

[sawtooth500]

Yeah basically it is a going to 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...

 

[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.