How to Calculate Initial Velocity in a Same Direction Crash Without Tire Marks?

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Discussion Overview

The discussion revolves around calculating the initial velocity of a vehicle involved in a same direction crash without tire marks or braking evidence. Participants explore the application of momentum principles in this context, considering the complexities introduced by the lack of certain data.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using the conservation of momentum to relate the velocities of the two vehicles before and after the collision, assuming car A hits car B from behind.
  • Another participant reiterates the momentum conservation principle, emphasizing that the total momentum before the impact equals the total momentum after the impact, but notes the need for specific values to solve for the initial velocity of car A.
  • A later reply questions the applicability of translation symmetry in this scenario, suggesting it may only hold in the Newtonian limit.
  • One participant expresses uncertainty about how to determine the pre-collision velocities without having the necessary values, mentioning an additional impact with a wall that complicates the analysis.

Areas of Agreement / Disagreement

Participants generally agree on the relevance of momentum conservation in analyzing the crash, but there is disagreement regarding the implications of translation symmetry and how it applies to the scenario. The discussion remains unresolved regarding the calculation of initial velocities without specific data.

Contextual Notes

Limitations include the absence of pre-collision velocity values for both vehicles, which are critical for applying the momentum conservation equations effectively. The discussion also highlights potential complexities introduced by subsequent impacts and the conditions under which translation symmetry applies.

Colm2243
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What formula(s) would I use to find the initial velocity of a vehicle that has impacted a second vehicle in a same direction crash. There are no tire marks on the roadway and no braking involved. Thanks.
 
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In physics, there is something called translation symmetry, meaning that the fundamental properties of the Universe does not depend on where you are. Out of this symmetry, a phenomena known as momentum arises. In non-relativistic velocities, this is a good approximation.

From your post, I assume that the first car (called car A) hits the second car (car B) from behind. No matter if some kinetic energy is converted to heat energy via friction, the sum of the momentum for car A and the momentum of car B before the impact is the same as the sum of the momentum for car A and the momentum for car B after the impact.

[tex]m_{A(before)} v_{A(before)} ~+~ m_{B(before)}v_{B(before)}~ = m_{A(after)} v_{A(after)} ~+~ m_{B(after)} v_{B(after)}[/tex]

Solve for the velocity for A before the crash if you have access to the other values.
 
Last edited:
Moridin said:
In physics, there is something called translation symmetry, meaning that the fundamental properties of the Universe does not depend on where you are. Out of this symmetry, a phenomena known as momentum arises. In non-relativistic velocities, this is a good approximation.

From your post, I assume that the first car (called car A) hits the second car (car B) from behind. No matter if some kinetic energy is converted to heat energy via friction, the sum of the momentum for car A and the momentum of car B before the impact is the same as the sum of the momentum for car A and the momentum for car B after the impact.

[tex]m_{A(before)} v_{A(before)} ~+~ m_{B(before)}v_{B(before)}~ = m_{A(after)} v_{A(after)} ~+~ m_{B(after)} v_{B(after)}[/tex]

Solve for the velocity for A before the crash if you have access to the other values.
I don't have the values for pre collision velocity on either vehicle. How can I determine this? A wall was impacted after the two vehicles became stuck together and after impact with the wall vehicle two separated and rolled over and skid to a stop 40 feet after separation on it' s roof.
 
Moridin said:
In non-relativistic velocities, this is a good approximation.
Translation symmetry only exists in the Newtonian limit?!?
 

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