Question

A 40 kg child moving at 3 m/s runs in a straight line and jumps on a 2 metre radius merry go round. The merry go round has inertia 55 kg m2. Find the heat energy created by this collision

answer: 46.05J

Answer 1

here,

mass of child , m1 = 40 kg

initial speed , u = 3 m/s

moment of inertia of merry-go-round , I = 55 kg.m^2

radius , r = 2 m

let the final angular speed be w

using conservation of angular momentum

m1 * u * r = (I + m1 * r^2) * w

40 * 3 * 2 = (55 + 40 * 2^2) * w

solving for w

w = 1.17 rad/s^2

the heat energy created by this collison , Q = the kinetic energy lost

Q = 0.5 * m1 * u^2 - 0.5 * (I + m1 * r^2) * w

Q = 0.5 * 40 * 3^2 - 0.5 * (55 + 40 * 2^2) * 1.17^2 J

Q = 32.84 J