Question

A 50 g marble moving at 2.2 m/s strikes a 23 g marble at rest. Assume the collision is perfectly elastic and the marbles collide head-on.What is the speed of the first marble immediately after the collision?What is the speed of the second marble immediately after the collision?

Answer 1

here,

mass of marble 1 ,m1 = 50 g

initial speed of 1 , u1 = 2.2 m/s

mass of marble 2 , m2 = 23 g

let the final speed after the collsion be v1 and v2

using conservation of momentum

m1 * u = m1 * v1 + m2 * v2

50 * 2.2 = 50 * v1 + 23 * v2 .....(1)

and

using conservation of kinetic energy

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

50 * 2.2^2 = 50 * v1^2 + 23 * v2^2 .....(2)

from (1) and (2)

v1 = 0.81 m/s

v2 = 3.01 m/s

the speed of the first marble immediately after the collision is 0.81 m/s

the speed of the seccond marble immediately after the collision is 3.01 m/s