Question

A toy cannon uses a spring to project a 5.21-g soft rubber ball. The spring is originally compressed by 4.99 cm and has a force constant of 7.93 N/m. When the cannon is fired, the ball moves 14.4 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 9 N on the ball. The maximun speed occurs 4.59 cm from its original position. What is this maximum speed?

Answer 1

here,

mass , m = 5.21 g = 0.00521 kg

spring constant , K = 7.93 N/m

initial compression , xi = 4.99 cm = 0.0499 m

final compression , xf = (4.99 - 4.59) = 0.4 cm = 0.004 m

frictional force , ff = 0.0319 N

let the maximum speed be v

using work energy theorm

work done by friction force = change in total energy

ff * s = 0.5 * k * ( xi^2 - xf^2) - 0.5 *m * v^2

0.0319 * 0.0459 = 0.5 * 7.93 * (0.0499^2 - 0.004^2) - 0.5 * 0.00521 * v^2

solving for v

v = 1.79 m/s

the maximum speed is 1.79 m/s