Question

A string of 4.00 cm long hangs from a ceiling with a ball attached to it. When the ball an the string are placed in a horizontal position and released from rest, the ball swings along an arc. How fast ( in m/s) is the ball going at the lowest point in its swing?

Answer 1

for calculation purpose, lowest point is taken as reference surface for height calculation for potential energy.

when string and ball are in horizontal position they will have gravitational energy only as they are released from rest.

so Ei = M *g * h here h = 4.00 * 10^-2 m

now when they both are at the lowest point, there will be kinetic energy only as they are at datum.

Ef = 1/2 * M * v^2

so conservation of energy ,

Ei = Ef

M *g * h = 1/2 * M * v^2

v = ( 2 * g * h )^1/2
= ( 2 * 9.8 * 4.00 * 10^-2 )^1/2

= 0.885 m/s