Car Collision - Which car was speeding?

[mAbubakr]

This problem is an equation derivation question. An equation needs to be derived. This equation is then used to make a procedure to find the required variables (You are an engineer onsite).

Homework Statement

Two cars collide on a road and leave skid marks on the road. They 'hook bumpers' and move as one. Derive and equation to calculate their initial velocities to find the speeding car.

Homework Equations

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂ '

The Attempt at a Solution

Key Assumptions:
1. The net force on the cars is zero.


m₁v₁ + m₂v₂ = m₁'v₁' + m₂'v₂ '

Since the cars move as one, we can put the speeds of both cars together:
m₁v₁ + m₂v₂ = (m₁ + m₂)(v')

Now I am not sure where to go from here because of many missing variables. The mass of the cars can be found by weighing them. Not sure about the final velocity, you just have skid marks on the road.

Any help would be appreciated. Thanks!

 

[BruceW]

The bit that you have done so far is correct. But obviously this is not enough to tell us which car was speeding (if any). In any case, what you are given is the skid marks, and this might not directly give you the final velocity anyway. The information about the skid marks will give the answer, but you haven't said anything about what the skid marks are like. To start the problem, you've got to be clear on what the question says about the skid marks.

 

[mAbubakr]

I wish I could be more specific but our teacher has not given us the question sheet. He simply read it out to us to give us hints as to where to focus on studying.

I assume the skid marks are created after the crash and can be used to represent the displacement of the cars after collision.

 

[BruceW]

maybe your teacher was just getting you guys to start thinking about this kind of problem. In this case, I'd say that the equation that you have given is the important equation for this situation. (Also need to consider that the cars will have motion in 2-d, so the equation will be a vector equation).

If the skid marks are created after the crash, you are totally right that they will represent the motion after collision.

 

[mAbubakr]

Can you lead me in the right direction? I've been trying to derive the equation but no luck. I'm still stuck with two variables. In this case I know I will have to derive another equation and sub it into the first. Substitution method is the only way I can think of.

I can't seem to see what the second equation would be. Would the use of the Ek = Ek' equation help? It also has velocity values present and might be possible to use those to isolate to only one equation.

Thanks!

 

[iRaid]

If you have the initial velocity and the length of the skid mark you can find the deceleration which will help you with the final speed.

 

[mAbubakr]

Hmm. The problem is what we are not given any values. All values have to be found on our own by assuming we are working as an engineer on the site. So we have to let the teacher know what we will do to find the value.

For example, mass is not given but I can say, "The mass can be found by weighing the cars".

I've thought about it a bit more and think the conservation of energy equations must be used. Since it will be a completely elastic collision (cars hook bumpers and move together) it will probably be something like so:

(1/2)(m)(v)² = F_fΔd

Now I am confused because this is the energy of the system. I am assuming this velocity would be of the cars when they move together.

After which I was thinking of isolating v in the above equation and subbing it back into the momentum equation to just have two missing variables (v1 and v2). Like BruceW said it should be in 2D so therefore I can use substitution to just get one variable. I think that makes sense but would love your opinions and ideas.

 

[SammyS]

There are skid marks. Suppose you can measure the skid marks. --- that should give three more pieces of data.