# Conservation of energy for a collision

#### Norules

1. Homework Statement
You are just starting a new job as investigator for the car collision investigation. You assist your superior in order to determine, as accurately as possible, the circumstances surrounding collisions (initial velocity of the vehicles involved, direction vehicles were heading, etc.) in order to determine whether the drivers at fault under the Criminal Code (dangerous driving causing death or other charges).
The weather is great and you arrive at the station as your boss tells you, “Hey, Daniel, hurry over to Jalan BBN 1/A. There has been an accident involving two cars. There are people injured.” You rush to the scene of the accident immediately. Your job is to take photos of the vehicles as they are positioned, and take a certain number of measurements, including the length of the skid marks and layout of the debris.
• Numerous debris (broken glass, plastic, etc.) were found at a distance of 12 m from the cars;
• The two cars stuck together (red car is heading to the black car) and there are skid marks over 12 m;
• There are also skid marks over a distance of 30 m before the debris;
• The posted speed limit on this street is 70 km/h;
• Other information: m1(red car) = 2500 kg, m2(black car) = 1100 kg.

Return to the station, your superior yells out, “Hey, Daniel, make yourself useful! Bring the friction block and spring scale, and take the measurements needed to calculate the pavement’s coefficient of friction.” Confused, but very eager, you take the heavy iron friction block, covered with tire treads, and the spring scale.
Your superior returns to you and says, “The two drivers aren’t saying much. The one in the black car was sent to the hospital. The driver in the red car is still discussing what happened, but nothing is clear!” Since you are always willing to help, you answer, “How can I help you, Sir?” Your superior’s face lights up when he hears your proposition, “Well, it’s that…, you see, we must be sure, beyond any doubt, that dangerous driving was involved… the judge needs evidence. We must gather all the necessary evidence. All I’m sure of is that, based on the skid marks, the black car was at the stop when the collision occurred. This a perfect job for an intern! Get to work! I want a full report as soon as possible”. Knowing that this information will decide whether the driver will be charged under Criminal Code, you take your role very seriously and immediately get to work.
Considering that the accident occurred in a 70km/h zone, what do you suggest to your superior? How would you clearly explain to your superior about the method used to determine the speed of the driver at fault?

Solve:

1. Calculate the velocities of two vehicles before and after impact using physics principles, such as forces, motion, mechanical energy, and conservation of momentum.
2. Explain how frictional forces related to varying surfaces affect the motion of an object.

2. Homework Equations
1)m1u1=(m1+u1)V1
2)W=Fnettd=$\Delta$KE

3. The Attempt at a Solution

From second equation:-

Fnett=mg=(3.5*10^4N)
W=W=Fnettd=(3.5*10^4N)(12m)=4.2*10^5 J
W=$\Delta$KE=$\frac{1}{2}$mv^2; 4.2*10^5 J=1/2(3.6*10^3)v^2
v= 1.5*10^1 m/s

thus the red car is travelling below the speed limit .
I did this question only until here as I was not sure of my answer.
Please point out errors and if not understood I attached an image.Thanks

NR

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#### haruspex

Homework Helper
Gold Member
2018 Award
You're image is very hard to read, so I may be misinterpreting.
It looks to me that you have calculated the work required to raise both vehicles vertically by 12m. There should be a reference to coefficient of friction. The text of the problem seemed to be leading up to a value for that but I don't see one. Have you left out some text?
Yiu are asked to explain your method to your superior. That would be a tood way to start your post, before getting into the algebra.
Also, when you do get into the algebra, always work symbolically, as though all the values are unknowns. Only plug in numbers at the end.

#### Norules

No reference of coefficient is given in this question :(

NR

#### haruspex

Homework Helper
Gold Member
2018 Award
No reference of coefficient is given in this question :(

NR
Then take the coefficient of kinetic friction to be an unknown μ. Create symbols for all the given data and see what equations you can develop.

#### Rellek

Looks like you've got four unknowns, and it is possible to create 4 equations.

#### Yashbhatt

Well, I think you have left out some data. If you have the initial velocity of the car which is moving then you can easily calculate μ using v2 -u2 = 2as , F = ma and F = μN.

#### haruspex

Homework Helper
Gold Member
2018 Award
Well, I think you have left out some data. If you have the initial velocity of the car which is moving then you can easily calculate μ using v2 -u2 = 2as , F = ma and F = μN.
Given the context in which the question is set, the initial velocity is the value to be calculated.

#### Yashbhatt

And how do we get the initial velocity?

#### Norules

I think the best way to go about this question is to assume the standard coefficient of kinetic friction to be 0.7,from there you can calculate acceleration using F-Ffr = ma, from here use V2=U2 -2as to find U ,since the final velocity is 0 so V=0 . From here to find the initial velocity of the red car just use the same formula but change S=30 m and you will find that the red car exceeds the speed limit.

Last edited:

#### haruspex

Homework Helper
Gold Member
2018 Award
I think the best way to go about this question is to assume the standard coefficient of kinetic friction to be 0.7,from there you can calculate acceleration using F-Ffr = ma, from here use V2=U2 -2as to find U ,since the final velocity is 0 so V=0 . From here to find the initial velocity of the red car just use the same formula but change S=30 m and you will find that the red car exceeds the speed limit.
Yes, except that you have not described how to obtain the red car's speed just before the collision from its speed just after the collision.
How about you post some equations and working? (Please keep it as purely symbolic algebra, as though you had no numerical values.)

"Conservation of energy for a collision"

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