# Combined problem: momentum & friction

I don't know how to approach the problem below:

An SUV and a car collide at a stoplight. The wreck slides to a complete stop.

mass SUV = 4200 kg
mass car = 2100 kg
velocity car = 0 m/s
distance the wreck slides = 12 meters
Mu = .65

Find the velocity of the SUV.

What I tried:

Since it crash is shown as being completely inelastic I know that both objects have the same velocity after the crash so I can treat their mass as one also.

First I set up an equation for the momentum:

p1 + p2 = p1 (prime) + p2 (prime)
[mass SUV * velocity SUV] + [mass car + velocity car] = vprime [mass SUV + mass car]

[4200 * velocity SUV] + 0 = 6300v(prime)

So from that equation I have two unknowns.

I know that the final velocity of the wreck is 0 and that the initial velocity before the slide is the same as Vprime.

The full body diagram that I drew for the wreck just before the slide has four forces acting upon the mass: Fg down, Fn up, the momentum to the right, and friction to the left.

After doing that I'm not sure where to go next.

Any ideas?

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Momentum is not a Force , so should not show up on a free-body diagram.
... but the average velocity after collision (during slide) is half the velocity just as the slide starts. So you can find the duration of the slide (a formula).

Friction times duration of slide is what changes the momentum after collision.
Insert the formula for duration, and solve for SUV speed.

(by the way, this is really a Work-Energy scenario, if you're doing that...)