Question

Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 270000 kg and a velocity of 0.325 m/s in the horizontal direction, and the second having a mass of 52500 kg and a velocity of -0.12 m/s in the horizontal direction. What is their final velocity?

Answer 1

0.252 m/s

Step-by-step explanation:

Applying the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

Note: From the question, The collision between the car and the train is an inelastic collision and as such, both move with a common velocity after collision.

mu+m'u' = V(m+m')................... Equation 1

Where m = mass of the train, u' = initial velocity of the train, m' = mass of the car, u' = initial velocity of the car, V = common velocity after collision.

make V the subject of the equation

V = (mu+m'u')/(m+m')............... Equation 2

Given: m = 270000 kg, u = 0.325 m/s, m' = 52500 kg, u' = -0.12 m/s

Substitute these values into equation 2

V = [(270000×0.325)+{52500(-0.12)}]/(270000+52500)

V = 81450/322500

V = 0.252 m/s