Question involving conservation law and springs

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Homework Help Overview

The discussion revolves around a problem involving a freight car colliding with a spring-loaded bumper. The scenario includes a mass of 1800 kg for the freight car and an 800 kg mass for the bumper, with the car's speed recorded at 4.2 m/s after the collision. Participants explore the application of conservation laws, particularly momentum and energy, to determine the initial speed of the freight car and the time taken to come to rest.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of conservation of momentum and energy, questioning the correct application of these principles. There are attempts to derive expressions for momentum before and after the collision, and some participants express confusion regarding the nature of the collision (elastic vs. inelastic). Questions arise about the role of the springs and how to calculate time based on the car's motion.

Discussion Status

The discussion is active, with various interpretations being explored. Some participants have provided calculations and expressed uncertainty about their correctness. Guidance has been offered regarding the application of conservation laws, and there is a focus on clarifying the relationship between the spring's behavior and the car's motion.

Contextual Notes

Participants note the lack of specific information about the spring constant, which is crucial for determining the period of oscillation. There is also an ongoing discussion about the assumptions made regarding the collision type and the implications for energy conservation.

  • #31
A freight car of mass 1800kg is timed at 4.2m/s just after it runs into a spring-loaded bumper at the end of the track. The bumper consists of an 800kg mass that the car runs into, and a pair of large springs. The car travels 2.4m before coming to rest.
 
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  • #32
And what are the questions that the problem asks?
 
  • #33
a)using an appropriate conservation law, find the speed of the freight car before it struck the bumper.
b)Find the time taken for the car to be brought to rest.
 
  • #34
OK. You can use energy conservation to find the spring constant k. You need to say that the mechanical energy immediately after the collision (when the spring is still uncompressed) is equal to the mechanical energy at maximum compression (when the masses are instantaneously at rest). This should give you k which you can then use to find the period.
 
  • #35
So...

PEs + KE = PEs + KE
0 +1/2mv^2 = 1/2kx^2 = 0

where v is the speed found from part a and x is the distance given before it comes to rest. Then find x and solve for T.

is that right?
 
  • #36
i'm sorry...the speed should be 4.2m/s because that is the speed right after collision.

I get a k of 7962.5N/m and therefore T = 3.60s

Can you confirm this?

THANKS FOR ALL YOUR HELP! =)
 
  • #37
Confirmed. Don't forget that 3.60 s is not the time you are looking for.
 

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