# How Fast Were the Cars Traveling Before the Collision?

• ilovemynny
In summary, the two cars involved in the accident had a total mass of 5000 kg and collided at an intersection with one car traveling North and the other East. The collision occurred in the middle of the intersection and both cars were locked together and slid a distance of 6.0 meters along a line that measured 40o North of East. Based on the coefficient of friction between the road and the sliding cars, the frictional force that stopped the cars was approximately 70,000 N. This resulted in an acceleration of 14 m/s/s for the sliding cars. The momentum of the two cars after the impact was 65,000 kg m/s, with Ed contributing 39,000 kg m/s and Ned contributing
ilovemynny

## Homework Statement

The Known Facts of the Accident

[1] Ned was traveling North on Oak Avenue in his car of mass 2000kg
[2] Ed was traveling East on King Street in his truck of mass 3000 kg
[3] The two approached the intersection at the same moment.
[4] With his stoplight “green”, Ned had the right-of-way and entered the intersection.
[5] Ed admitted that he failed to stop for the light and entered the intersection at the same moment as Ned.
[6] The collision occurred in the middle of the intersection.
[7] Both cars locked together upon impact and slid to a stop.
[8] From the point of impact (determined by shattered headlights on the pavement), the cars traveled a distance of 6.0 meters along a line that measured 40o North of East.
[9] From data tables in their accident investigation manuals, the investigators determined that the coefficient of friction between the road and the sliding cars was 1.5

[A] Considering the road surface to be horizontal, what was the frictional force that acted upon the locked sliding cars to stop them?

What was the magnitude of the acceleration that this force produced on the sliding cars sliding together?

[C] Based upon the stopping distance from the point of impact and the acceleration, what was the speed of the two locked cars at the moment after the impact?

[D] What was the momentum of the two locked cars at the moment after the impact?

[E] What part of this momentum did Ed contribute? (this would be his momentum before impact)

[F] What part of this momentum did Ned contribute?

[G] What was Ed’s speed before the collision?

[H] What was Ned’s speed before collision?

The speed limit at the intersection was 35 mi/hr. The police will ticket drivers for speeding if they exceeded the speed limit by more than 5 mi/hr. Should either of the two drivers be ticketed for speeding? Defend your answer with calculations.

## The Attempt at a Solution

So these are the questions I've already got to:

My Work:

A) To find the friction force I used this formula: Ff = coefficient of friction x mass x 9.81
So my friction force came out to be 73575 N which turned into 70,000 N because of significant numbers.

B) F = m x a so 70000 = 5000a and a = 14 m/s/s

C) vf^2 = vi^2 + 2ad
vf^2 = 2 x (14)(6)
vf^2 = 168
vf = 12.96
vf = 13 m/s

D) Momentum: P = m x v
P = (2000 + 3000) kg x (13 m/s)
P = 65000 kg m/s

E) Momentum of Ed: P = m x v
P = 3000 kg x 13 m/s
Ed: P = 39000 kg m/s

F) Momentum of Ned: P = m x v
P = 2000 kg x 13 m/s
Ned: P = 26000 kg m/s

I just don't know how to find their initial speed?
And I feel like I didn't do E and F right.

ilovemynny said:
E) Momentum of Ed: P = m x v
P = 3000 kg x 13 m/s
Ed: P = 39000 kg m/s
Sorry, but you'll need to rethink the above. Remember, momentum is a vector, like velocity. But this 13 m/s figure, as you've expressed it above is a speed.

To determine the momentum in the East direction, you'll need to take that "40o North of East" statement into consideration somehow.

And the mass is not just Ed's car. You're calculating the North component of the total wrecked mass. So you'll need to get the mass of Ted's car back in there too.

Think of it another way. You already know the magnitude (which you've calculated) and direction (given in the problem) of the total momentum after the collision. Break this total momentum vector into its x and y components for parts E) and F).
F) Momentum of Ned: P = m x v
P = 2000 kg x 13 m/s
Ned: P = 26000 kg m/s
Same comments as above. You'll need to take the "40o North of East" statement into consideration to determined the North component of the momentum. Mass is the total mass, not just Ted's car.

I just don't know how to find their initial speed?
Once you have each car's respective momentum, you can use $\vec p = m \vec v$ to get each car's respective initial velocity.
[Edit: This is step where you can use the individual masses of the respective cars.]

Last edited:

## 1. What is "Finding Speed Before Crash"?

"Finding Speed Before Crash" is a scientific process used to determine the speed of an object before it experiences a crash or collision. This information can be useful for accident reconstruction and determining the cause of the crash.

## 2. How is speed before crash calculated?

Speed before crash is calculated using physical principles such as conservation of momentum and energy. This involves collecting data such as the distance traveled, time of impact, and mass of the object to determine its velocity before the crash.

## 3. What are the limitations of calculating speed before crash?

There are several limitations to calculating speed before crash, including human error in collecting and recording data, uncertainties in the initial conditions of the object, and the complexity of real-world collisions. Additionally, the accuracy of the calculation depends on the availability and quality of data.

## 4. How is this information used in accident investigations?

The speed before crash can provide crucial evidence in accident investigations, especially in cases where there are no eyewitnesses. It can help determine who was at fault and assist in determining the cause of the accident. This information can also be used in court proceedings to determine liability and potential damages.

## 5. Can speed before crash be determined for all types of collisions?

While speed before crash can be determined for most collisions, there are some cases where this may not be possible. For example, if the collision involves multiple objects or complex dynamics, it may be challenging to accurately calculate the speed before crash. Additionally, if there is insufficient data available, it may be impossible to determine the speed before crash.

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