A golf ball with mass m = 0.05 kg is tied to a massless string of length L = 0.28 m. The ball is made to swing in a circle such that the string is horizontal throughout the motion. The ball makes one revolution every t = 2.1 s.
m = 0.05 kg
L = 0.28 m
t = 2.1 s
Fnet = mv2/r
The Attempt at a Solution
(a) What the magnitude of the tension in the string, Ft in Newtons, while it spins?
First, I made it so that one revolution would occur at the bottom of the circle which is created by the ball swinging, so that it would be a little easier mathematically.
I identified Fnet as the Tension of the string on the ball pulling upward (TSB) minus the weight of the Earth on the ball (WEB). The rearranged equation looks like this:
TSB - WEB = mv2/r
Then I rearranged it to look like this:
TSB = mv2/r + WEB
Since Weight = mg...
TSB = mv2/r + mg
With that, I plugged in my numbers:
TSB = (.05kg)v2/(.14m)+ (.05kg)(9.8 m/s2)
I got the radius by dividing the length by two...though I'm not sure if this is right. Plus, there doesn't seem to be any information about the velocity. How would I go about finding this? Would I use a = ΔV/t?
(b) The string breaks suddenly. How fast does the golf ball fly away, v in m/s?
What accounts for the string breaking? How do I know which direction the string is flying in? Would it matter in this case if the string was flying in a positive direction or a negative direction?