Question

Two objects moving with a speed v travel in opposite directions in a straight line. The objects stick together when they collide, and move with a speed of v/4 after the collision. Part A What is the ratio of the final kinetic energy of the system to the initial kinetic energy? V AO O ? Submit Request Answer Part B What is the ratio of the mass of the more massive object to the mass of the less massive object? O A O ? Submit Request Answer

Answer 1

here,

let the mass of massive be M and less massive be m

using conservation of momentum

M * v - m * v = (m+ M) * v/4

(M - m) * v = ( m + M) * v/4

4 M - 4 m = m + M

3 M = 5 m

M/m = 5/3 = 1.67 ....(1)

a)

the final kinetic energy of the system to the initial kinetic energy , R = (0.5 * (m + M) * (v/4)^2 ) /(0.5 * m * v^2 + 0.5 * M * v^2)

R = ((m + 1.67 m) * (v/4)^2 ) /( m * v^2 + (1.67 m) * v^2)

R = ((1 + 1.67 ) * (1/4)^2 ) /( 1 + (1.67 ) * 1^2)

R = 6.25 * 10^-2

b)

from (1)

M/m = 1.67