Car collision skid mark physics

[whereisccguys]

Your friend has just been in a traffic accident and is trying to negotiate with the insurance company of the other driver to pay for fixing her car. She believes that the other car was speeding and therefore the accident was the other driver's fault. She knows that you have a knowledge of physics and hopes that you can prove her conjecture. She takes you out to the scene of the crash and describes what happened. She was traveling North when she entered the fateful intersection. She looked in both directions and did not see another car approaching. It was a bright, sunny, clear day. When she reached the center of the intersection, her car was struck by the other car which was traveling East. The two cars remained joined together after the collision and skidded to a stop. The speed limit on both roads entering the intersection is 50 mph. From the skid marks still visible on the street, you determine that after the collision the cars skidded 56 feet at an angle of 30 degress north of east before stopping. She has a copy of the police report which gives the make and year of each car. At the library you determine that the weight of her car was 4000 lbs and that of the other car was 3600 lbs, where you included the driver's weight in each case. There were no other passengers. The coefficient of kinetic friction for a rubber tire skidding on dry pavement is 0.8. The other driver's insurance agent, trying to find an excuse to deny claim to your friend, insists that it is not enough to prove his client was speeding, so your friend must also show that she was under the speed limit.
find the speed of your friend's car and the speed of the other driver's car

so first i have to find out the speed right after they crash into each other goin in the 30 deg direction
so i set kinetic energy = the work done by friction since that's the only force there
1/2mv^2-1/2mVinitial^2=-0.8(mg)*D D is the distance traveled after the crash

since v=0 at that point 1/2 Vinitial^2=0.8(g)*D
Vinitial = sqrt(2*0.8*g*D)

and then this part I'm not too sure if it is right

m1v1 = (m1+m2)v cos 30 m1 is the car goin east
m2v2 = (m1+m2)v sin 30

and i plug and solve but i still get the wrong answer... anyone know what i did wrong

okay... nevermind i did a really stupid mistake i switched m1 and m2 so i kept gettin the opposite answer... sorry

 

[Curious3141]

I get about 67 mph for the eastward driver, and 35 mph for your friend. Is that correct ?

Basically all you need is conservation of momentum and a simple equation of motion.

Let the final velocity of the two car fused combination be v.

Before the collision, your friends car had only northward momentum, the other car, only eastward. Treat those directions as perpendicular axes.

Set up momentum conservation equations in each axis. You'll get two equations. The left hand side of each equation will have the momentum of each car before the collision. The right hand side will have the component of momentum after the collision in that axis.

To find the magnitude of the final velocity v, use $$v^2 = u^2 + 2as$$. Basically, you're considering that the frictional force is acting to decelerate the mass to a stop in a certain distance, which is given (from the skid marks). a, the acceleration is equal to frictional force divided by the combined mass of the vehicles. The frictional force can be found by the coefficient of friction and the normal force. Here you should set initial velocity to be v (what you want to find) and the final velocity to be zero.

Try again and see if you get the correct answer.

EDIT : Never mind, I read your post and you've done everything right (you used conservation of energy instead of an equation of motion, but that's fine). Did you get the correct answer ?

 

[whereisccguys]

yea i got the right answer... but thanks anyways

 

[HallsofIvy]

The worst thing your friend can do is say she "did not see another car". No matter how fast the other car was going, it couldn't have come from so far away she couldn't see it. Legally, how fast the other car was going is irrelevant. If, as I surmise from what you said, your friend was at a stop sign, the other car had the right of way and it was your friends responsibility to make CERTAIN that there was no other car coming.

 

[Curious3141]

The worst thing your friend can do is say she "did not see another car". No matter how fast the other car was going, it couldn't have come from so far away she couldn't see it. Legally, how fast the other car was going is irrelevant. If, as I surmise from what you said, your friend was at a stop sign, the other car had the right of way and it was your friends responsibility to make CERTAIN that there was no other car coming.

Yes, this is why I hate this sort of verbose problem. With all due respect to the "enlightened educators" out there trying to make Physics/Math more interesting to "pragmatic" students with "real world problems", I get bored to tears :zzz: and irritated trying to read through long winded problems that are only there to pad up the mathematics. Plus, there's always the danger of coming up with a trivial and completely non-mathematical solution, as you did ! (that is, whichever car ran the stop sign is at fault, full stop).

Do you remember the guy who got the question : "how would you measure the height of a tall building with an aneroid barometer ?", and answered : "I would tie the aneroid barometer to a long string, lower it from the top of the building to the ground like a plumbline and measure the length of the string" ? It IS a perfectly valid answer !

If you want kids to solve problems with simple physical problems, just state them with economy of language. There is nothing to be gained by making the problem appear to be a philosophy question.

 

[HallsofIvy]

To be honest, I had forgotten it was a "homework problem" when I responded! I was thinking this guy was actually trying to plan a defense!

 

[Curious3141]

^^Now that is funny.