A car of mass 1800 kg stopped at a traffic light is struck from the rear by a 90

Question

A car of mass 1800 kg stopped at a traffic light is struck from the rear by a 900-kg car, and the two became entangled. A) If the smaller car was moving at 20.0 m/s before the collision, what is the velocity of the entangled cars after the collision? b) What would be the final speed if the two cars each had a mass of 900 kg? The collision shown in fig.2 is completely in elastic. The bodies are attached after the collision. M_A = 5kg, M_B = 3kg, V_A1 = 3m/s, V_s1 = 2 m/s A) What is the final velocity of bodies A and B after the collision? B) Compute the total K.E. before the collision and the total K.E. after the collision. C. Find the ratio of the final K.E. of the system, to the initial K.E. of the system D. Find the energy lost if V_A1 was originally at rest and bodies are attached after the collision.

Explanation / Answer

2)

The collision is inelastic collision

Momentum is conserved.

a)

m1v1+m2v2 = (m1+m2)v

v = 900*20/2700 = 6.66 m/s

b)

v = 900*20/1800 = 10 m/s

3) Let final velocity be v

v = m1v1+m2v2/(m1+m2)

v = (15-6)/8 = 1.125 m/s

b)

Final KE after collision = 1/2 (m1+m2)*v^2 = 4*1.125^2 = 5.0625 J

Initial KE = 1/2 m1v1^2+1/2m2*v2^2 = 1/2 (45+12) = 28.5 J

c)

KE final/ KE initial = 5.0625/28.5 = 0.177

d) Initial energy = 1/2 m2v2^2 = 6J

Final KE = 5.0625 J

Energy Lost = 6-5.0625 = 1.0625 Joules

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