Question

A 5.0-kg mass moving at 8.0 m/s collides head-on with a 3.0-kg mass initially at rest If the collision is perfectly elastic, what is the speed of the masses just after the collision? Is the kinetic energy conserved?

Answer 1

here,

the mass of first object , m1 = 5 kg

the mass of second object , m2 = 3 kg

initial velocity of first , u1 = 8 m/s

let the final velocity of each object be v1 and v2

using conservation of momentum

m1 * u1 = m1 * v1 + m2 * v2

5 * 8 = 5 * v1 + 3 * v2 ......(1)

and

using conservation of kinetic energy

0.5 * m1 * u1^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

5 * 8^2 = 5 * v1^2 + 3 * v2^2 ......(2)

from (1) and (2)

v1 = 2 m/s

v2 = 10 m/s

the final velocity of 5 kg object is 2 m/s

the final velocity of 3 kg object is 10 m/s

as the collison is perfectly elastic

the kinetic energy remains conserved