Inelastic Collisions in One Dimension

beatbama85

Here's my problem:

Car A (mass 970 kg) is stopped at a traffic light when it is rear-ended by car B (mass 1600 kg). Both cars then slide with locked wheels until the frictional force from the slick road (with a low mk of 0.23) stops them, at distances dA = 5.8 m and dB = 3.6 m. What are the speeds of (a) car A and (b) car B at the start of the sliding, just after the collision? (c) Assuming that linear momentum is conserved during the collision, find the speed of car B just before the collision.

The name of the section that this problem corresponds to is the title of this thread. I know about the conservation of momentum (ma(va1) + mb(vb1) = ma(va2) + mb(vb2), where a and b are the cars and 1 and 2 is initial and final) and the equation for the center-of-mass velocity ((pa1 + pa2)/(ma + mb)), but I don't know what to do with the friction. Should I find the frictional forces and integrate them to get the final momentums?

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beatbama85

Nevermind, I can't believe I didn't think of this earlier. I just realized that, after the collision, the kinetic energy transfers completely to thermal energy, so I was able to find va2 and vb2 from K = 1/2v^2. Then, applying the equation for conservation of momentum, I was able to find vb1.

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