Question

A ball swings in a vertical circle at a constant speed at the end of a 1.5-m-long string. When the ball is at the top of the circle, the tension is 10N, at the bottom the tension is 50N.

a) What is the mass of the ball?

b) What is the speed of the ball?

Answer 1

r = length of string
= 1.5 m
when ball is at top
T and m*g both are in same direction
so,
centripetal force = T+m*g
(m*v^2)/r = T+m*g
(m*v^2)/1.5 = 10 + m*9.8

when ball is at bottom
T and m*g are in opposite direction
so,
centripetal force = T+m*g
(m*v^2)/r = T - m*g
(m*v^2)/1.5 = 50 - m*9.8

a)
dividing first equation by second
we get,
1 = (10 + m*9.8)/(50 - m*9.8)
50 - m*9.8 = 10 + m*9.8
40 = 2*m*9.8
m = 2.04 g

b)
put the value of m in below equation
(m*v^2)/1.5 = 10 + m*9.8
(2.04*v^2)/1.5 = 10 + 2.04*9.8
(1.36*v^2) = 10 + 20
(1.36*v^2) = 30
v^2 = 22.1
v = 4.70 m/s