As shown in the figure below, we have three air carts (labeled #1, #2, and #3) o

Question

As shown in the figure below, we have three air carts (labeled #1, #2, and #3) on an air track. The carts are equipped with spring bumpers so that all collisions are elastic. The masses of the carts are

m1 = 4m, m2 = 2m,

and

m3 = m.

Initially, cart #1 is given a velocity to the right of magnitude

v0

and the other carts are at rest. Determine the following.

(a) final speed of each cart (Indicate the direction with the sign of your answer.)

(b) ratio of the total kinetic energy before any collision to the total kinetic energy after all collisions

Please show your work if possible, thank you very much!!

Explanation / Answer

m1= 4*m

m2 = 2m

m3 = m

a) final speed of cart 1,

v1 = (m1-m2)*vo/(m1+m2)

= (4*m - 2*m)*vo/(4*m + 2*m)

= (2/3)*vo <<<<<<<<-----------------Answer

speed of cart 2 after colliding with m1,

u2 = 2*m1*vo/(m1+m2)

= 2*4*m*vo/(4*m+2*m)

= 1.333*vo

speed of cart after making collsion with cart 3

v2 = (m2 - m3)*u2/(m2+m3)

= (2*m - m)*1.333*vo/(2*m+m)

= 0.444 *vo(final speed) <<<<<<<-----------------Answer

final speed of cart 3,

v3 = 2*m2*u2/(m1+m2)

= 2*2*m*1.333*vo/(2*m+m)

= 1.78*vo <<<<<<<-----------------Answer

b) KEi/KEf = 1

beacuse all the collsions are elastic

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