Question

A railroad car of mass 2.50 3 104 kg is moving with a speed of 4.00 m/s. It collides and couples with three other coupled railroad cars, each of the same mass as the single car and moving in the same direction with an initial speed of 2.00 m/s. (a) What is the speed of the four cars after the collision? (b) How much mechanical energy is lost in the collision?

Answer 1

Answer:2.5 m/s

37.5KJ

Step-by-step explanation:

Let
`u_1, u_2 , v_f` be the initial velocity of rail road car ,coupled cars & Final velocity of system respectively.

`m=2.50* 10^(4)`

Conserving momentum

`mu_1+3mu_2=4mv_f`

`4m+6m=4mv_f`

`v_f=2.5 m/s`

Therefore Final velocity of system is 2.5m/s

(b)Mechanical Energy lost =Initial Kinetic Energy -Final Kinetic Energy

`Initial Kinetic Energy=(1)/(2)m\left ( 4^2\right )+(1)/(2)m\left ( 2^2\right )=14m J`

`Final Kinetic Energy=(1)/(2)4m\left ( 2.5^2\right )=12.5m J`

`Mechanical Energy lost=14m-12.5m=3.75* 10^4=37.5 KJ`