A railroad car of mass M moving at a speed v1 collides and couples with two coup

Physics
Tutor: None Selected Time limit: 1 Day

A railroad car of mass M moving at a speed v1 collides and couples with two coupled railroad cars, each of the same mass M and moving in the same direction at a speed v2.

(a) What is the speed vf of the three coupled cars after the collision in terms of v1 and v2?
vf
 

(b) How much kinetic energy is lost in the collision? Answer in terms of Mv1, and v2.
 
Jun 8th, 2015

Thank you for the opportunity to help you with your question!

momentum will be conserved after collision. Therefore, p(i) = M*v1 + M*v2 +M*v2 and p(f)=(M+M+M)*Vf

Vf =(M*v1+M*v2+M*v2)/(3M) = (v1 +2*v2)/3, since M*v1+M*v2+M*v2 is the momentum after collision.

b) the kinetic energy:

K(i)=1/2*M*v1^2 +1/2*M*v2^2 +1/2*M*v2^2

K(f)= 1/2*M/3*[v1^2 +4*v1*v2+4*v2^2] 

therefore energy lost= K(f)-K(i)

=1/2*M*v1^2 +1/2*M*v2^2 +1/2*M*v2^2-{1/2*M/3*[v1^2 +4*v1*v2+4*v2^2]}

=M/3*[-v1^2 + 2*v1*v2 -v2^2]

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 8th, 2015

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