# Accident Reconstruction; Work-Energy Problem

• uchicago2012
In summary, the problem involves reconstructing a car accident and determining the car's initial speed based on skid marks and coefficient of friction. The solution involves calculating the work done by friction using the equation Wnon = KE2 - KE1 + PE2 - PE1, and using the fact that the car is on a flat surface and stays on a flat surface, so the change in potential energy is equal to 0. The final answer is found by calculating the friction for each tire using 1/4 of the weight of the car as the normal force, and using the equation ƒ•d = (0.92)(1/2)(1600)(9.81)(18) = 129830.4
uchicago2012

## Homework Statement

Accident Reconstruction.
A car, with a mass of 1600 kg, is involved in a collision. By using techniques from later chapters, we conclude it was moving 4 m/s at impact. There are skid marks leading into the collision, 18 meters long from two of the tires; no marks from the other two. If the coefficient of friction from the pavement is .92, how fast was the car going before skidding?

## Homework Equations

Wnon = Change in KE + Change in PE

## The Attempt at a Solution

I found the work done by the force of friction so I can use this equation:

Wnon = KE2 - KE1 + PE2 - PE1
where Wnon = work done by friction
but I was wondering if there were any other nonconservative forces I had to worry about. In these types of problems do you only account for things like air resistance if it specifically tells you to or should I just assume air resistance is part of the Wnon?

Also, since the car is on a flat surface and stays on a flat surface, Change in PE = 0, correct?

I guess I just expected this problem to be more difficult and I'm nervous I've missed something.

dude i think I'm in your class, that is if you go to USI. this is what i got not sure if it's right though.

Fr = μN

N = the normal force

Since only two tires were involved in the skid, the normal force is not going to equal the entire weight of the car, assuming the car is perfectly symmetrical, it will be half.

Fr = μ(½mg)

Energy = ƒ•d = (0.92)(1/2)(1600)(9.81)(18) = 129830.4 J

The same amount of energy expressed as a difference in kinetic energy...

½m(v1)² - ½m(v2)²

v1 = starting velocity
v2 = final velocity

129830.4 = ½(1600)(v1)² - ½(1600)(4)²

v1 = 13.4 m/s
this could be wrong and I'm not sure if we can use the idea of using 1/2 the weight of the car to find the Normal force.

Wouldnt it be 1/4 of the weight of the car per tire instead of 1/2 of the weight of the car per tire?

It is. It's 1/4 the weight per tire but there's two skid marks so there's two tires so it's 1/2 the weight of the car.
I'm just not sure we can assume that we use half the weight instead of all the weight.

That's an interesting idea and it is a bit odd how it specifically mentions there are only two tire tracks. But for a rear wheel drive car there would only be two tire tracks and I don't know that you would calculate the weight differently for a rear wheel drive than for say an all wheel drive car.

I feel like there are two sources of friction, one from each tire. So perhaps calculate the friction for each tire using one fourth of the weight of the car as the normal force? Which is pretty much the same thing you did by halving the weight.

Or would we calculate the friction from each tire using the entire weight of the car?

Hmm.

Anyone have any suggestions?

I believe the way renee did the problem is correct. Thats going to be my answer.

## 1. What is accident reconstruction?

Accident reconstruction is the process of using scientific principles to investigate and analyze the events that led to an accident. This can include gathering evidence, examining physical damage, and using mathematical equations to reconstruct the sequence of events.

## 2. Why is accident reconstruction important?

Accident reconstruction is important because it can help determine the cause of an accident, which is crucial in determining liability and preventing future accidents. It can also provide valuable information for legal cases and insurance claims.

## 3. What is the work-energy problem in accident reconstruction?

The work-energy problem in accident reconstruction refers to the principle that the work done on an object is equal to the change in its kinetic energy. This is important in analyzing accidents involving two or more vehicles or objects in motion.

## 4. How is the work-energy problem applied in accident reconstruction?

In accident reconstruction, the work-energy problem is applied by calculating the work done by a vehicle or object on another object, which is equal to the change in its kinetic energy. This can help determine the speed and direction of the objects involved in the accident.

## 5. What are some challenges in accident reconstruction involving the work-energy problem?

One of the main challenges in accident reconstruction involving the work-energy problem is obtaining accurate and reliable data, such as vehicle speeds, road conditions, and impact forces. Another challenge is accounting for all the variables and uncertainties that can affect the outcome of the reconstruction.

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