Physics problem help --- finding velocity after elastic collision given mass and initial velocity?

Question

A cart with mass m = 3.02 kg and initial velocity of v = 2.52 m/s collides with another cart of mass M = 4.92 kg which is initially at rest in the lab frame. The collision is completely elastic, and the wheels on the carts can be treated as massless and frictionless. What is the velocity of m in the center of mass frame after the collision?

Picture to go with problem: http://i284.photobucket.com/albums/ll28/bathtub2008/showmepl-2.gif

vf* = _____ m/s

Answer 1

notation:

carts 1 and 2: in lab frame 1 is initially moving, 2 is at rest

Vi1lab = initial V of cart 1 in the lab frame

Vi2lab = initial V of cart 2 in the lab frame

Vi1com = initial V of cart 1 in the center of mass frame

Vf1com = final V of cart 1 in the center of mass frame

Vcom = velocity of the center of mass in the lab frame

First find Vcom:

Vcom = (Vi1lab*m+Vi2lab*M)/(m+M)

=(2.52m/s*3.02kg)/(3.02kg+4.92kg)

=0.958m/s

Now find Vi1com:

Vi1com = Vi1lab - Vcom = 2.52m/s - 0.958m/s = 1.56m/s

Because we have a totally elastic collision and we are using a COM frame:

Vf1com = -Vi1com = -1.56m/s

So the answer is -1.56m/s.