Expert: Sherman D. - 11/6/2005

Question
A ball of mass 0.50kg is swung in a circule of radius 2.0m with a period of 1.5s (as in figure #028) Then it is a picture of a mass being swung in a circle tied to a string going through a glass tube than another mass is tied to the other end.
Here's the picture: http://www.smgaels.org/physics/home/lab/Centripetal_Force_Lab_files/image001.jpg
a) what is the speed of the ball?
b) what is the accleration of the ball?
c) what centripetal force must be exerted by the string that keeps the ball in orbit?
d) what is the mass of the central object?
e) what angle does the string make with the vertical?
f) how long is the string, L?  

Answer
Assuming the radius remains the same and the period remains constant.

a.)
v = 2pi(r/T)
v = 2pi(2/(1.5))
v = 2pi(2/(3/2))
v = 2pi((2/1)/(3/2))
v = 2pi((2/1)*(2/3))
v = 2pi(4/3)
v = ((8pi)/3) m/s
v = 8.38 m/s

b.)
Ac = (v^2)/r
Ac = (((8pi)/3)^2)/2
Ac = ((64pi^2)/9)/2
Ac = ((64pi^2)/9)/(2/1)
Ac = ((64pi^2)/9)*(1/2)
Ac = (64pi^2)/18
Ac = (32/9)pi^2 m/s^2
Ac = 35.09 m/s^2

c.)
Fc = mv^2/r
Fc = .5(32/9)pi^2
Fc = (1/2)(32/9)pi^2
Fc = (32/18)pi^2
Fc = (16/9)pi^2 (kg * m)/(s^2)
Fc = 17.55 (kg*m)/s^2 or 17.55N

I'm not totally certain about d-f.