The mass of the railway carriage is 8000 kg which is movinig with the speed of `54 km h^(-1)` collides with the another stationary carriage of same mass. Determine the loss in kinetic energy in this process.

Explanation

Given, `m_(1) = 8000kg`
`v_(1) = 54 kmh^(-1) = 54 xx (5/18)ms^(-1) = 15ms^(-1)`
`m_(2) = 8000kg, v_(2) = 0`
By conservation of momentum,
`m_(1)v-(1) + m_(2)v_(2) = (m_(1) + m_(2))v`
`v=(m_(1)v_(1))/(m_(1) + m_(2)` `[therefore v_(2) =0]`
`= (8000 xx 15)/(8000+8000) = 7.5 ms^(-1)`
Loss of kinetic energy = KE before collision - KE after collision
`=(1/2)m_(1)v_(1)^(2) - (1/2)(m_(1) + m_(2))v^(2)`
`=(1/2) xx 8000 xx(15)^(2) - (1/2)(8000 + 8000)(7.5)^(2)`
`= 400 xx 225 - 8000 xx 56.25`
`=450 kJ`