Consider a collision of air carts in a system similar to the one below, which ar

Question

Consider a collision of air carts in a system similar to the one below, which are equipped to stick together upon touching. Suppose the air cart to the left has a mass of m1 = 0.640 kg and an initial speed of 0.410 m/s. The cart to the right is initially at rest, and has a mass of m2 = 0.325 kg.

(a) Find the velocity of the center of mass before the carts collide and stick together. (m/s)
(b) Find the velocity of the center of mass after the carts collide and stick together. (m/s)
(c) Find the kinetic energy of the system before and after the collision.
J (before)
J (after)

Explanation / Answer

m1 = 0.64 kg, m2 = 0.325 kg, u1 = 0.41 m/s

u2 = 0

(a) Vcm = m1u1 +m2u2/(m1+m2)

Vcm = (0.64*0.41+0)/(0.64+0.325)

Vcm = 0.272 m/s

(b) From conservation of momentum

m1u1 +m2u2 = (m1+m2)v

0.64*0.41 +0 = (0.64+0.325)v

v = 0.272 m/s

(c) KEi = (1/2)m1u1^2 +(1/2)m2u2^2

= 0.5*0.64*0.41^2 +0

KEi = 0.054 J

KEf = (1/2)(m1+m2)v^2

= 0.5*(0.64+0.325)0.272^2

= 0.036 J

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