Look at the diagram below. Carts A and B can roll freely and without friction on

Question

Look at the diagram below. Carts A and B can roll freely and without friction on the level track. Cart B has twice the mass of cart A. Suppose that cart A is moving at a velocity (V_Ai) when it collides with cart B (initally at rest). After the collision, Cart A is moving at one-third of its original speed but in the opposite direction.

(a) What is the relationship between the final velocities of the two carts? Justify your answer, using the conservation of Linear Momentum to write an appropreate eqation, then rearranging it to make your point. Show all of your work.

Explanation / Answer

Conservation of linear momentum implies

MA*VAi=-(1/3)*MaVAi+MB*VBf-----------------------------------(1)

VBi=0

using

MB=2*MA

from (1) we get

(4/3)*MA*VAi=2*MA*VBf

hence

VBf=(2/3)*VAi

the final velocity of Cart B is two-thirds of the initial velocity of Cart A.

(b) I should position Cart A on the left-end side of the track and the initial position of cart B should be (2/3) of LT (of the right side of the track), so after the colision occurs the carts will reach the opposite end of the track at the same time.

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