A car of mass m moving at a speed v 1 collides and couples with the back of a tr

Question

A car of mass m moving at a speed v1 collides and couples with the back of a truck of mass 4m moving initially in the same direction as the car at a lower speed v2. (Use any variable or symbol stated above as necessary.)

(a) What is the speed vf of the two vehicles immediately after the collision?
vf =

(b) What is the change in kinetic energy of the car–truck system in the collision?K=

A railroad car of mass 2.60 104 kg is moving with a speed of 3.88 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 1.94 m/s.

Explanation / Answer

(a) from conservation of momentum

mcv1 + mtv2 = (mc + mt)*vf

vf = (mcv1 + mtv2) / (mc + mt)

= (mv1 + 4mv2) / (m + 4m)

vf = (v1 + 4v2) / 5 ..................ans

(b) change in kinetic energy = (1/2)*(mc + mt)*v2f - ((1/2)*mc*v21 + (1/2)*mt*v22)

= (1/2)*5m* (v1 + 4v2)2 / 25 - ((1/2)*v21 + (1/2)*4*v22)m

=(1/10)*m*((v1 + 4v2)2 - 5*(v21 + 4*v22))

=(1/10)*m*( 8v1v2 - 4v21 - 4v22)

= -(2/5)*m*( v1 - v2)2 ....................ans

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