Question

A mass is moving at 7 m/s in the +x direction and it collides in a...

A mass is moving at 7 m/s in the +x direction and it collides in a perfectly elastic collision with a mass of 2 kg moving in the -x direction. The collision takes places in 0.19 seconds and after the collision the mass that was moving in the +x direction is moving in the -x direction at 9 m/s and the mass that was moving in the -x direction is moving in the +x direction at 15 m/s. What is the magnitude of the average force, in Newtons, on the first mass which was originally moving in the +x direction before the collision?

here,

initial speed of 1 ,u1 = 7 m/s

initial speed of 2 is u2

mass of 2 , m2 = 2 kg

final speed of 1 , v1 = - 9 m/s

final speed of 2 , v2 = 15 m/s

using conservation of momentum

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

m1 * 7 + 2 * u2 = - m1 * 9 + 2 * 15 .....(1)

and

using conservation of kinetic energy

0.5 * m1 * u1^2 + 0.5 * m2 * u2^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

m1 * 7^2 + 2 * u2^2 = m1 * 9^2 + 2 * 15^2 .....(2)

from ( 1) and (2)

m1 = 4 kg

u2 = - 17 m/s

the impulse delivered to 1 , I1 = m1 * ( v - u)

I1 = 4 * ( -9 - 7) = - 64 kg.m/s

time taken , t = 0.19 s

the magnitude of the average force on m1 , F1 = |I1| * t

F1 = 64 * 0.19 = 12.16 N