Trying to find equations to use for calculation of initial speeds

[BeanBolta]

Homework Statement

Hello all, I'll try to keep this as short as possible! :) I won't include the particular values we were given, just so I still have to do something for this part. It shouldn't matter too much, I believe.

My team and I are acting "car crash investigators" for the purpose of this task, and were given a scenario where the following happened;
One car is approaching an amber light at a crossroad with the intent to go through straight ahead, but the driver thinks they see a car coming from the wrong direction on the crossroad (both are one way streets - red herring maybe) and panic brakes. They skid to a halt in the middle of the intersection.

A second car is coming down the road (also heading straight ahead), crossing the road the first car is traveling on. They don't slow down because it's night time and the driver of the second car can see from a reflection that the other light is amber, so their light will change to green by the time they get to the intersection (and it does), however before he can pass the lights, he sees a car has skidded to a halt in front of him and he crashes into the first car, which causes the first car to spin around to some other angle. After the crash the second car then coasts a certain distance away.

The information we are given (I won't put down the numbers so I'm not getting out of all the work :)
- Length of the straight skid marks of BOTH cars.
- Length of the curved skid marks of the FIRST car, which it created when spinning after being hit.
- Width of the streets
- Distance between the stop line for each set of traffic lights and the (imaginary) edge of the crossing road ahead.
- The distance the second car coasted (no braking) after crashing.

This last is the bit that's throwing us off. We are able to calculate the initial velocity of both cars, IF they both come to rest upon crashing, however the second car does not (rolls a given distance away before stopping) and I'm not sure how to find out how much left over energy it had after crashing into the first car (and hence making it coast for a distance afterwards).

Homework Equations

F_Fn=u*(m*g), where F_Fn is the force of friction, and u is the friction coefficient.
a=F_Fn/m, to find the acceleration
V_F^2=V_0^2+2as, to find the initial velocity (works fine for the first car, however does not take into account the coasting after crashing of the second car.)
V_F=V_0+at --> t=u/a, to find the time elapsed during deceleration (V_F = 0, hence removed from equation)
s=1/2(V_0+V_F)*t, to double check the skid mark distance against information provided. My result agreed with the skid mark length we were given, hence my decision not to include figures.

The Attempt at a Solution

We have been able to obtain reasonable answers for all equations concerning the first vehicle, however are stuck on the second car which crashes into the first stationary car, as it has some left over velocity, which we do not know how to calculate.

Thanks very much for any words of wisdom (and sorry for the extremely long post :)!

:Edit:
Also, we thought of using the work equation;
1/2m_yv_y=Fd+u --> 1/2*m_y*v_y=(m_g*g*d)+((mu*m_y)*g*s) --> v_y=sqrt((m*g*d)+(mu*g*s)/(0.5*m_y)) , with y and g being the car colours (Stationary = green, Crasher = yellow), however this also assumes the second car comes to a complete stop in assuming the work done to spin the first car is equal to the momentum (and hence velocity) of the second vehicle.

 

[gneill]

Homework Statement

Hello all, I'll try to keep this as short as possible! :) I won't include the particular values we were given, just so I still have to do something for this part. It shouldn't matter too much, I believe.

My team and I are acting "car crash investigators" for the purpose of this task, and were given a scenario where the following happened;
One car is approaching an amber light at a crossroad with the intent to go through straight ahead, but the driver thinks they see a car coming from the wrong direction on the crossroad (both are one way streets - red herring maybe) and panic brakes. They skid to a halt in the middle of the intersection.

A second car is coming down the road (also heading straight ahead), crossing the road the first car is traveling on. They don't slow down because it's night time and the driver of the second car can see from a reflection that the other light is amber, so their light will change to green by the time they get to the intersection (and it does), however before he can pass the lights, he sees a car has skidded to a halt in front of him and he crashes into the first car, which causes the first car to spin around to some other angle. After the crash the second car then coasts a certain distance away.

The information we are given (I won't put down the numbers so I'm not getting out of all the work :)
- Length of the straight skid marks of BOTH cars.
- Length of the curved skid marks of the FIRST car, which it created when spinning after being hit.
- Width of the streets
- Distance between the stop line for each set of traffic lights and the (imaginary) edge of the crossing road ahead.
- The distance the second car coasted (no braking) after crashing.

This last is the bit that's throwing us off. We are able to calculate the initial velocity of both cars, IF they both come to rest upon crashing, however the second car does not (rolls a given distance away before stopping) and I'm not sure how to find out how much left over energy it had after crashing into the first car (and hence making it coast for a distance afterwards).

Homework Equations

F_Fn=u*(m*g), where F_Fn is the force of friction, and u is the friction coefficient.
a=F_Fn/m, to find the acceleration
V_F^2=V_0^2+2as, to find the initial velocity (works fine for the first car, however does not take into account the coasting after crashing of the second car.)
V_F=V_0+at --> t=u/a, to find the time elapsed during deceleration (V_F = 0, hence removed from equation)
s=1/2(V_0+V_F)*t, to double check the skid mark distance against information provided. My result agreed with the skid mark length we were given, hence my decision not to include figures.

The Attempt at a Solution

We have been able to obtain reasonable answers for all equations concerning the first vehicle, however are stuck on the second car which crashes into the first stationary car, as it has some left over velocity, which we do not know how to calculate.

Thanks very much for any words of wisdom (and sorry for the extremely long post :)!

:Edit:
Also, we thought of using the work equation;
1/2m_yv_y=Fd+u --> 1/2*m_y*v_y=(m_g*g*d)+((mu*m_y)*g*s) --> v_y=sqrt((m*g*d)+(mu*g*s)/(0.5*m_y)) , with y and g being the car colours (Stationary = green, Crasher = yellow), however this also assumes the second car comes to a complete stop in assuming the work done to spin the first car is equal to the momentum (and hence velocity) of the second vehicle.

Hi BeanBolta, Welcome to Physics Forums.

If the second car coasts without breaks or friction on a flat surface, what is to prevent them coasting indefinitely? (Hint: why were you given the geometry and dimensions of the intersection?)

 

[BvU]

Dear cci, (welcome to PF)

You have the skid marks of the second car, but throughout the story there is no point where I read that it is braking too. Strange. After crashnig, it still doesn't brake and coasts on. Why does it stop at a certain point at all ?

Did the police officers provide you with a detailed sketch summarizing all the long-worded info, or did you have to make it yourself ? Either way, perhaps you want to post it too !

Furthermore, you have to make a lot of assumptions, e.g. about friction coefficients when skidding in the driving direction vs same when spinning. Right ?

 

[haruspex]

e.g. about friction coefficients when skidding in the driving direction vs same when spinning. Right ?

I don't see why those friction coefficients would be much different. A bigger problem is that the front and rear tyres will skid for different distances, and we don't know the weight distribution between them.

 

[HalfLostAndSearching]

As a scientist, it is important to use equations and mathematical models to accurately analyze and predict real-world phenomena. In this case, your approach to finding equations to calculate initial speeds in a car crash scenario is a good start. However, there are a few things to consider in order to improve your analysis.

Firstly, it is important to understand the limitations of the equations you are using. For example, the equation V_F^2=V_0^2+2as assumes that there is no external force acting on the object other than the force of friction. In a real-world scenario, there may be other factors at play such as air resistance or the deformation of the cars upon impact. Therefore, it is important to consider all possible factors and their effects on the final results.

Secondly, it is also important to accurately measure and record all the necessary variables in order to obtain accurate results. In this case, you mentioned that the distance the second car coasted after crashing was throwing off your calculations. It may be helpful to obtain more accurate measurements for this distance in order to get a more precise result.

Additionally, it may be beneficial to use more advanced equations and models that take into account the dynamics of the crash, such as the conservation of momentum and energy. These equations can provide a more comprehensive analysis of the scenario and may help to explain the coasting distance of the second car after the crash.

In conclusion, using equations and mathematical models is a crucial part of being a scientist, but it is important to use them accurately and consider all factors in order to obtain reliable results. Keep exploring and trying different approaches to find the best solution for this scenario. Good luck!