Circular Motion Problem: Finding Tension in a Vertical Circle [11.8 N]

[PhysicStud01]

Homework Statement

object of mass 0.20 kg tied to a string is made to move in a vertical circle. When the object is at the highest point, the tension in the string is zero. Determine the tension in the string when the object is at the lowest point. [11.8 N]

Homework Equations

The Attempt at a Solution

i tried it and could not arrive at the state answer in bracket. at highest point, weight + tension gives the centripetal force. since tension is said to be zero, at the hioghest point, weight = centripetal force.

then at lowest point, tension - weight gives centripetal. tension is the sum of centripetal and weight = 2 x weight since centripetal was calculated to be equal to weight. but this is not the answer given.
am i missing something?

 

[Suraj M]

Your right about the first part. But the centripetal force acting on the body is not a constant.

At the highest position
T=0
mg = v²/r
v =√gr
this velocity is not the same velocity which it has at the lowest position
To calculate that use the law of conservation of energy :
½mv²_{highest position} = ½mv²_{lowest position} + mg(2r)
and then find your tension.

 

[DEvens]

<snips>
T = 11.8 N
okay?

You did pretty much the entire problem. You did it well but you did too much. Let the OP do his own homework and just give hints.

I know there is an urge to leap out and solve the problem. I have the same urge. But once you solve it, don't post the entire thing. If you do the entire thing for them they won't get the benefit of the homework.

 

[Suraj M]

You did pretty much the entire problem. You did it well but you did too much. Let the OP do his own homework and just give hints.

I know there is an urge to leap out and solve the problem. I have the same urge. But once you solve it, don't post the entire thing. If you do the entire thing for them they won't get the benefit of the homework.

ok DEvens .. i realized that and edited it ..and sorry.

 

[HalfLostAndSearching]

Your approach is correct, but there may be a mistake in your calculations. The tension at the lowest point should be equal to the sum of the weight and the centripetal force, not double the weight. Double-check your calculations and equations to see if there was a mistake made. It's also possible that the given answer of 11.8 N may be incorrect.