Question

A 500 gram mass is connected to a spring and undergoing uniform circular motion. The radius is at 14.5 cm and the applied centripetal force is 5.88N. The velocity of the spinning mass is measured to be 1.31 m/s. Keeping the force and mass constant the radius of the bob was increased by 1 cm. What should be the expected velocity of the spinning mass at the new radius?

Answer 1

To solve the problem it is necessary to apply the concepts related to the Centripetal Force.

By definition the centripetal force is given by

$F_c = \frac{mv^2}{R}$

Our values are defined by

$m=0.5Kg\\F_c = 5.88N \\R = 0.145m+1cm = 0.155m\\v = 1.31m/s$

Therefore replacing in the equation we have to,

$F_c = \frac{mv^2}{R}$

$5.88=\frac{0.5*v^2}{0.155}$

Re-arrange to find V,

$V=\sqrt{\frac{5.88*0.155}{0.5}}$

$V= 1.35m/s$

Therefore the expected velocity of the spinning mass at the new radius is 1.35m/s