Question

Two masses m1= 4kg and m2=12kg collide head on both masses where initially moving in a positive direction with velocity of 24 meter per seconds and 8 meter per seconds respectively. Calculate the velocity each of the masses after the collision assuming that the collision is elastic

Answer 1

In an elastic collision, both momentum and kinetic energy are conserved.

The total momentum before the collision is given by:
m1*u1 + m2*u2 = 4*24 + 12*8 = 96 + 96 = 192 kg m/s

Where:
m1 = 4kg (mass of first object)
u1 = 24 m/s (velocity of first object)
m2 = 12kg (mass of second object)
u2 = 8 m/s (velocity of second object)

Let the velocities of the two masses after collision be v1 and v2.

According to the conservation of momentum:
m1*v1 + m2*v2 = 192

Given an elastic collision, the conservation of kinetic energy holds true as well:
1/2 * m1 * u1^2 + 1/2 * m2 * u2^2 = 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2

Plugging in the given values:
1/2 * 4 * 24^2 + 1/2 * 12 * 8^2 = 1/2 * 4 * v1^2 + 1/2 * 12 * v2^2
1/2 * 4 * 576 + 1/2 * 12 * 64 = 2 * v1^2 + 6 * v2^2
2 * 576 + 6 * 64 = 2 * v1^2 + 6 * v2^2
1152 + 384 = 2 * v1^2 + 6 * v2^2
1536 = 2 * v1^2 + 6 * v2^2

Now we have a system of two equations:

m1*v1 + m2*v2 = 192
2 * v1^2 + 6 * v2^2 = 1536

Solving these two equations simultaneously gives:
v1 = 12 m/s
v2 = 24 m/s

Therefore, after the collision, the 4kg mass has a velocity of 12 m/s and the 12kg mass has a velocity of 24 m/s.