Physics spring/crate hits another spring problem

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Homework Help Overview

The problem involves a crate interacting with two springs on a frictionless surface, focusing on the compression of the second spring and the speed of the crate upon impact. The context includes concepts from mechanics, specifically energy conservation and spring dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the calculations for parts (a) and (b), with one participant expressing uncertainty about the variable x in their energy equation. There is also a consideration of potential energy in the first spring and its relevance to the problem.

Discussion Status

The discussion is ongoing, with participants exploring the implications of their calculations and questioning the setup of the problem. Some guidance is provided regarding the state of the springs at the moment of impact, but no consensus has been reached on the correct approach.

Contextual Notes

Participants note that the first spring is not explicitly stated to be attached to the crate, which raises questions about the energy transfer and potential energy involved in the scenario.

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Homework Statement


A crate of mass m = 0.29 kg is set against a spring with a spring constant of k1 = 581 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2 = 246 N/m.

(a) How far, d2 in meters, will the second spring compress when the crate runs into it?

(b) How fast, v in meters per second, will the crate be moving when it strikes the second spring?

(c) Now assume that the surface is rough (that is, not frictionless). You perform the experiment and observe that the second spring only compresses a distance d2/2. How much energy, in joules, was lost to friction?

Homework Equations


W=change in mech energy=Kf+Uf-Ki-Ui

The Attempt at a Solution


[/B]
I already calculated part a to be 0.1537. I just don't know how/if it relates to part b.

So far I have .5mv^2+.5kx=2.905 for part b. I'm just unsure what x is supposed to be or if I even set it up correctly.
 
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MattNguyen said:
I'm just unsure what x is supposed to be
So am I. It's your equation.
First, I assume you meant x2. Secondly, at the point in time indicated for part b, neither spring is under compression.
 
Yeah, that's what I meant. The first spring is stretched, though, so I'm assuming it has potential energy.
 
MattNguyen said:
Yeah, that's what I meant. The first spring is stretched, though, so I'm assuming it has potential energy.
It does not say it is attached to the first spring, merely pushed against it.
 

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