Question

A 0.25kg ball moving in a horizontal cirlce at the end of a string has a centripetal acceleration of 4m/s^2. What is the magnitude of the centripetal force exerted by the string on the ball to produce this acceleration?

Answer 1

Magnitude of the centripetal force exerted by the string on the ball to produce this acceleration which is given as :

centripetal force given by, F_c = m v² / r                                                      { eq.1 }

centripetal force given by, a_c = v² / r                                                               { eq.2 }

equating above two eq. we get

F_c = m a_c                                                                       { eq.3 }

where, m = mass of the ball = 0.25 kg

a_c = centripetal acceleration = 4 m/s²

inserting the values in eq.3,

F_c = (0.25 kg) (4 m/s²)

F_c = 1 N