Conservation of Momentum problem

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Homework Help Overview

The problem involves a collision between two cars, one traveling north and the other east, and seeks to determine their final velocity after they stick together. The subject area pertains to the conservation of momentum and vector analysis in physics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to treat the velocities as vectors rather than scalars, with some exploring how to calculate the final velocity and direction using vector components. Questions arise regarding the correct method for determining the angle of the resultant velocity.

Discussion Status

Some participants have provided guidance on treating the problem as a vector question, suggesting that the north-south and east-west components should be handled separately. There is ongoing exploration of how to accurately determine the angle of the final velocity.

Contextual Notes

Participants note the importance of specifying the angle in relation to the north-south direction and discuss the conventions for calculating angles in this context. There is a recognition of potential confusion regarding the components used in the tangent function.

Arooj
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Homework Statement


A 1500-kg car is traveling north at 25 m/s when it strikes a 2000-kg car traveling east at 20 m/s. The cars stick together after the collision. What is the final velocity of the two cars?


Homework Equations


m1v1 + m2v2 = (m1 + m2)vf


The Attempt at a Solution


1500(25) + 2000(20) = (1500 + 2000)vf
vf = 22.14 m/s

The answer was incorrect. I then thought vectors would be needed but wasn't sure. Can someone guide me through this problem?
 
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You've used the formula as for scalars, which assumes all movement is in the same dimension. Yes, it's a vector question. Treat NS and EW separately.
 
Thanks, I did so and found the final velocity to be 15.66 m/s. I'm confused on how to find the correct angle to use though for the direction is it the tan x comp over the y comp or the other way around? And how would you know which one it is?
 
Arooj said:
I'm confused on how to find the correct angle to use though for the direction is it the tan x comp over the y comp or the other way around? And how would you know which one it is?
It is standard to give priority to NS, so you should specify the angle as a deviation, E or W, from one of those. That means the tan of the angle will be x over y, in contrast to normal mathematics. You can check whether you have it the right way round by simply seeing which component is the greater and whether the angle is more or less than 45 degrees.
 

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