Kinetic Energy/Linear Momentum

[shaggyace]

Homework Statement

Three air carts have masses denoted as m, 2m, and 4m, all lined up one after another ron an air track. Initially, the cart denoted as 4m is at rest, whereas the other two carts are moving toward the cart at rest with a speed, v0 . All carts are equipped with putty bumpers that give completely inelastic collisions.

a. Find the final speed of the carts expressed through the given variables.

b. Calculate the ratio of the final kinetic energy of the system to the initial energy

Homework Equations

vf= (m1v1,i + m2v2,i) / m1+m2

KE=0.5(m)v^2

The Attempt at a Solution

I already got the first part. I worked it out to 3v0/7.
Im having trouble deriving the second part. I think I found the final kinetic energy as 1.5mV0
But I can't find the initial kinetic energy. What would be included in terms of mass? Is it the first two carts that are initially moving? or all the masses? and if so, how would you combine the zero velocity of the larger cart with the initial nonzero velocities of the other two carts. I am really confused with this part.

 

[Doc Al]

I think I found the final kinetic energy as 1.5mV0
But I can't find the initial kinetic energy.

That looks like the initial KE to me. How did you arrive at it?

(To find the total KE at any point, just find the KE of each mass and add them up. If something's not moving, what would be its KE?)