Conservation of Momentum - Collisions

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Homework Help Overview

The problem involves a collision between a truck and a car, where the conservation of momentum is applied to determine the velocity vector of the car after the collision. The scenario includes specific masses and velocities of both vehicles, as well as their directions of travel.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply the conservation of momentum to find the car's velocity after the collision and presents a calculated result for verification.
  • Some participants question the validity of the original poster's result, suggesting that it may violate principles of energy conservation.
  • Others clarify the notation used for directional angles and discuss the implications of momentum conservation versus energy conservation in this context.

Discussion Status

The discussion includes various interpretations of the problem, with some participants providing insights into the conservation laws involved. There is no explicit consensus on the correctness of the original poster's calculations, and concerns about the physical plausibility of the results have been raised.

Contextual Notes

Participants are navigating the complexities of vector components and the implications of conservation laws in collisions, with some expressing confusion over the direction notation and its impact on calculations.

doug1
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Homework Statement



A truck (4 000 kg) runs a red light and enters an intersection traveling at 81 km/h [E]. The truck collides with a car (2
000 kg) that was traveling at 54 km/h [N20oW]. Immediately after the collision the truck was traveling at 60 km/h [N
30o E]. Determine the velocity vector of the car immediately after the collision.


Homework Equations



I used the law of conservation of momentum. I used the concept that momentum is conserved in each component direction.

The Attempt at a Solution



The answer that I got was a velocity of approx 99 km/h [E32S]. Can anyone confirm this?
 
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This would violate energy conservation, unless the truck or the car have some active system to kick away other vehicles.
I don't understand the notation for the direction, but I would expect that momentum is not conserved either.
 
The notation [N30E] means 30 degrees east of north for example.

Momentum is conserved in this question, but energy is not
 
I agree that kinetic energy does not have to be conserved, but kinetic energy cannot increase in the process.

Working in units of 1000kg*km/h:
to east:
truck initial 4*81=364
car initial -2*54*sin(20°)
truck final 4*60*sin(30°)
car final ~207 or 104 km/h
Hmm... looks wrong.

to north:
truck initial 0
car initial 2*54*cos(20°)
truck final 4*60*cos(30°)
car final -106 or -53km/h

Total energy initially: 2*81^2+1*54^2=16000 (in 1000kg*(km/h)^2)
Total energy finally: 2*60^2+1*(104^2+53^2) = 20800
Clearly this cannot happen in a car accident. The same problem appears with your result of 99km/h total speed as well.
 
Last edited:

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