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 = 0.866 kg and an initial speed of 0.411 m/s. The cart to the right is initially at rest, and has a mass of m2 = 0.300 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

(A) Vcm = (m1 v1 + m2 v2 ) / (m1 + m2)

= (0.866 x 0.411 + 0 ) / (0.866 + 0.300)

= 0.305 m/s

(b) from momentum conservation,

velocity of centre of mass does not change during collision.

Vcm = 0.305 m/s

(c) Ki = (0.866 x 0.411^2 / 2 ) + (0 )

= 0.073 J

Kf = (0.866 + 0.300) (0.305^2) / 2

= 0.054 J

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