A train of mass 50,000kg and velocity of 30m/s collides with a stationary carraige of mass 10,000 kg. after the collision,both the train and the carraige moves off together as one body.determine the loss of kinetic energy due to the collision?

momentum is conserved

50000 * 30 = (50000 + 10000) * v
...1500000 = 60000 v ... v = 25

initial KE ... 1/2 * 50000 * 30^2

final KE ... 1/2 * 60000 * 25^2

To determine the loss of kinetic energy due to the collision, we need to calculate the initial kinetic energy before the collision and the final kinetic energy after the collision.

The initial kinetic energy is given by the formula:

KE1 = (1/2) * m1 * v1^2

where m1 is the mass of the train and v1 is the velocity of the train before the collision.

Plugging in the values:

m1 = 50,000 kg
v1 = 30 m/s

KE1 = (1/2) * 50,000 * (30^2) = 22,500,000 J

The final kinetic energy is given by the formula:

KE2 = (1/2) * (m1 + m2) * v2^2

where m2 is the mass of the carriage and v2 is the velocity of the train and carriage together after the collision.

Plugging in the values:

m2 = 10,000 kg (mass of the carriage)
v2 = ?

Since the train and the carriage move off together as one body, we can assume that their final velocity (v2) is the same. Let's denote it as V.

Therefore:

m1 * v1 = (m1 + m2) * V

50,000 kg * 30 m/s = (50,000 kg + 10,000 kg) * V

1,500,000 kg·m/s = 60,000 kg * V

V = 1,500,000 kg·m/s / 60,000 kg = 25 m/s

Now we can calculate the final kinetic energy:

KE2 = (1/2) * (50,000 kg + 10,000 kg) * (25^2) = 7,500,000 J

The loss of kinetic energy is the difference between the initial and final kinetic energy:

Loss of KE = KE1 - KE2 = 22,500,000 J - 7,500,000 J = 15,000,000 J

Therefore, the loss of kinetic energy due to the collision is 15,000,000 Joules.