Homework Help: Normal force of a ball at the top and bottom of a circular path

oadeyemi · Mar 8, 2010

1. The problem statement, all variables and given/known data
A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming that the total energy of the ball-Earth system remains constant, show that the tension in the string at the bottom is greater than the tension at the top by six times the weight of the ball.

2. Relevant equations

See below...

3. The attempt at a solution
I tried to use W = ∆K = mgy and W₁ + U₁ + W = W₂ + U₂ to solve the problem,
but it did not work out.

I'm pretty lost on this one.

HELP!!!

rl.bhat · Mar 9, 2010

Minimum velocity of the ball at the top of the circular motion is given by
m*vi^2/R = mg = T Or vi^2 = Rg.
When it falls to the lowest point, let its velocity be vf and displacement be 2R.
Now apply the conservation of energy to find vf.
What is the tension in the string at the bottom of the circular motion of the ball?

oadeyemi · Mar 9, 2010

Thanks.. but I still don't quite see how to obtain the solution.

rl.bhat · Mar 9, 2010

vf^2 = vi^2 + 2*g*2R
Bur vi^2 = gR. So
vf^2 = gR + 4gR = 5gR
So the centripetal acceleration is 5g and gravitational acceleration is g.
So the total acceleration at the bottom is = ......
Compare it with that of at the top.

oadeyemi · Mar 9, 2010

rl.bhat said: ↑

vf^2 = vi^2 + 2*g*2R
Bur vi^2 = gR. So
vf^2 = gR + 4gR = 5gR
So the centripetal acceleration is 5g and gravitational acceleration is g.
So the total acceleration at the bottom is = ......
Compare it with that of at the top.

When I use the conservation of energy equation, do I account for T on both sides?

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Homework Help: Normal force of a ball at the top and bottom of a circular path

oadeyemi

rl.bhat

oadeyemi

rl.bhat

oadeyemi