Homework Help: Circular motion of ball and string

1. Feb 13, 2012

ScienceGeek24

1. The problem statement, all variables and given/known data

Part A : A 0.5 Kg ball is attached to a cord 80 cm long. The ball is whirled in a vertical circle at a constant speed. If the ball takes 0.4 seconds to go around once, what is the tension in the cord at the top and bottom of the circle?

Part B How long does it take for the ball to go around once if the tension in the cord at the top of the circle is zero?

2. Relevant equations
v=2Pi*R/T
T=m(g+v^2/r) (bottom of the circle)
T=m(g-v^2/r) (top of the circle)

3. The attempt at a solution

For part A i used both of the circular motion formulas to fin the tension and i got totally different answers from what it suppose to be for top and bottom. Top it suppose to be 93.8N and bottom it suppose to be 104 N i got 92.7N top and 102.7 N bottom. ( I do not know if the answer is a print error).

For part A I tried to use v=2Pi*R/T to get the time and i keep getting the same time in part A which is 0.4 secs. But the answer is 1.8 seconds.

Can someone explain to be what I'm doing wrong??? thanks!

2. Feb 13, 2012

tony24810

the formula for top of the circle should be

T=m(v^2/r - g) (top of the circle)

for part a, the time is 12.57 second

g = 9.81

try to put the numbers in your calculator more carefully, the result should come out correct

3. Feb 13, 2012

tony24810

for part b, tension must equal zero yet F=ma must be obeyed

F = m * a

T + mg = m * v^2/r (the downward force consist of tension and weight)

mg = m*v^2/r (T=0)

g = v^2/r

v = 2.8 m s^-1

now try the v=2Pi*R/T again

4. Feb 13, 2012

ScienceGeek24

Thanks it worked!!!