3.) Cart A has mass 0.700 kg and initially moves at 2.60 m/s in the positive xdi

Question

3.) Cart A has mass 0.700 kg and initially moves at 2.60 m/s in the positive xdirection. Cart B has mass 0.400 kg and initially moves at 1.70 m/s in the negative xdirection.

a.) Suppose you attach Velcro to the carts so they collide in completely inelastic collision. Find the velocity of the carts immediately after the collision. (10 pts)

b.) Suppose you attach springs to the carts so they collide in a completely elastic collision. Find the velocity of each cart immediately after the collision. (15 pts)

Explanation / Answer

a) inel;astic collision
   miu1 + m2u2 = (m1+m2)V
   V = [0.7*2.6 - 0.4*1.7]/[0.7+0.4] = 1.036 m/s towards right
b) Elastic collision
   m1u1 + m2u2 = m1v1 + m2v2
   0.7*2.6 - 0.4*1.7 = 0.7*v1 + 0.4*v2 = 1.14
   v1 = (1.14 - 0.4v2)/0.7 = 1.628 - 0.57v2
   by energy conservation
   0.7(2.6)^2 + 0.4(1.7)^2 = 0.7(v1)^2 + 0.4(v2)^2 = 5.888 = 1.85 + 0.627v2^2 - 1.29v2
    0.627v2^2 - 1.29v2 -4.038 = 0

   v2 = 3.767 m/s
   v1 = -0.51919 m/s

   or v2 = -1.709 m/s
   v1 = 2.60213 m/s

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