Question

A 732kg parked car is rear-ended by a 1720kg truck moving at 15.5m/s. The truck smashes into the car and they slide along together. How far will they slide, if the coefficient of friction with the road is 0.70?

Answer 1

So first off you need to look off and imagine what's going on so that you can solve the problem. I broke it up into a few parts that I've drawn out.
Does that look like anything familiar to you?

M1V1+M2V2=(M1+M2)Vf
The formula for a perfectly inelastic collision. Why is it called perfectly inelastic? Because if it wasn't then they wouldn't stick together and it'd only be partially inelastic. If it was elastic they would bounce completely off each other.

So what do we know from the information given to us? The mass of the car is 732kg and its speed is 0m/s (at rest, don't forget!), the mass of the truck is 1720kg and it's moving 15.5m/s. So that satisfies the entire left hand side of the equation and the combined masses of the right hand side, so we can solve for the final velocity after the collision!

Now, what's the point of finding the final velocity? Well the point of the problem is to look at the distance it skids after impact. So we need the formula for work, which is Work = Force x Change in distance. That change in distance is going to be our final answer, so somehow we need to find the Work (Which is just the amount of energy) and the Force (Which is supplied by friction and gravity!)

So to satisfy this equation we've been given the friction coefficient which is .70 and we know that the formula for force of friction looks like this: Force is = coefficient * normal force. What's the normal force? Normal force is equal in magnitude to the force of gravity, all it's saying is the same force pulling the mass down, the mass is pushing back with. So now that we know that's equal we can substitute it into our equation from earlier...


Good, so now we just need the 'W' of the equation to solve for the distance. Work is just the amount of energy, and as we know, What does the "m" of the equation mean? The sum of the masses that are skidding to a halt from friction and that final velocity from earlier of inelastic collision.

Altogether you might have a formula that looks like this:

Looking at the fraction we see something interesting, the masses divide out since m/m =1 so we can see that the masses of the cars have no impact on how far they skid.

I've explained enough for you to figure this out on your own I think, good luck! If things are still unclear I'd be happy to explain them further. Also, I'm just a college student so don't think I'm Isaac Newton or anything cause I have been wrong in the past. Good luck!