# Free body diagrams with tension

1. Jul 21, 2007

My question is for free body diagrams with tension on top and mass hanging from the bottom. Why is it "T-mg" sometimes and "mg-t" other times. How do I know which one to use? I was doing gravitation questions where "T-mg=Fc" sometimes and "mg-t=Fc" other times.

2. Jul 21, 2007

### SpitfireAce

the net centripetal force is in the direction of the centripetal acceleration... if the thing is at the top, the centripetal acceleration is downward, and thus the gravitational force is winning (it must be in order to make the net force point down), so the gravitational force is greater and comes before tension...

Last edited: Jul 21, 2007
3. Jul 22, 2007

hmm im still kinda confused on this one..

4. Jul 22, 2007

### Dick

So are we. What is the difference between T and t? You haven't described the problem at all well.

5. Jul 22, 2007

### SpitfireAce

T is tension... he's referring to one of those ferris wheel problems asking what is the force of tension on the carriage while it is at the top/bottom of the revolution... I messed up on my answer because I thought you would get the gist so I didn't worry about the details... Fc=mv^2/r .... now lets say the mass is at the bottom of the revolution like you said, now lets find the net force. The force of tension and the force of gravity are in opposite directions (tension up, towards the center, and gravity down) so you know to subtract... but which to subtract from which... You want the net force to be positive, so if they tell you both forces just put the bigger one first... but let's say you're solving for tension. How do you know if tension is bigger and you should write T-mg=mv^2/r or gravity is bigger and you should write mg-T=mv^2/r.. if you don't know how big tension is... well the way to find out is to look at which direction the centripetal force needs to be pointing... the centripetal net force should always point to the center, so if the mass is at the bottom like we assumed you know that the net centripetal force should be pointing... up.... well since the net force must point up (and must be positive), you know that the force of tension must be greater than the force of gravity... thus you use T-mg... that's your answer... using mg-T in this case would give you a) a negative net force or b) a net force pointing away from the center ...thats bad

btw, disregard my post above, if the mass is at the top of the revolution, both the force of gravity and force of tension would be pointing down and the net force would just be T+mg

Last edited: Jul 22, 2007
6. Jul 23, 2007