A railroad car of mass 2.51 104 kg is moving with a speed of 3.92 m/s. It collid

Question

A railroad car of mass 2.51 104 kg is moving with a speed of 3.92 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 1.96 m/s.

A railroad car of mass 2.51 x 104 kg is moving with a speed of 3.92 m/s. It collides and couples with three other coupled railroad cars, each of the same mas as the single car and moving in the same direction with an initial speed of 1.96 m/s (a) What is the speed of the four cars after the collision? (Round your answer to at least two decimal places.) m/s (b) How much mechanical energy is lost in the collision?

Explanation / Answer

Using momentum conservation:

Pi = Pf

m1v1 + m2*v2 = (m1 + m2)*V

V = (m1v1 + m2v2)/(m1 + m2)

m1 = 2.51*10^4 kg

m2 = 3*m1

v2 = 1.96 m/sec

v1 = 3.92 m/sec

V = (2.51*10^4*3.92 + 3*2.51*10^4*1.96)/(4*2.51*10^4)

V = 2.45 m/sec

B.

Energy lost = KEi - KEf

dKE = 0.5*m1v1^2 + 0.5*m2*v2^2 - 0.5*(m1 + m2)*V^2

dKE = 0.5*m1*(v1^2 + 3*v2^2 - 4*V^2)

dKE = 0.5*2.51*10^4*(3.92^2 + 3*1.96^2 - 4*2.45^2) = 36159.06 J

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