a) Consider the collision of two carts of identical masses m . Before the collis

Question

a) Consider the collision of two carts of identical masses m. Before the collision, cart 2 is at rest and cart 1 is moving towards cart 2 with constant velocity v1i. Assume that collision is inelastic (that is two carts stick together after the collision), after the collision both carts are moving with the same velocity v1f=v2f. Find out v1f in terms of initial velocity v1i and carts' masses m. Presume original direction of cart 1 to be positive.

b) Now if cart 1 is twice as heavy so that its total mass is 2m and cart 2 still has mass m, write down the equations for v1f if cart one is still moving with the same initial velocity v1i before the collision and cart 2 is initially at rest.

Explanation / Answer

(a) v2i =0

Accoring to conservation of momentum

m1v1i+0 =(m1+m2)v1f

v1f = m1v1i/(m1+m2)

m1 =m2 =m

v1f = v1i/2

(b) v2i =0

Accoring to conservation of momentum

m1v1i+0 =(m1+m2)v1f

v1f = m1v1i/(m1+m2)

m1 =2m, m2 =m

v1f = 2mv1i/(2m+m)

v1f = 2v1i/3

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