Finding the distance a spring compresses

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Homework Help Overview

The problem involves an object of mass 2.2 kg moving on a horizontal surface with a coefficient of kinetic friction of 0.2. It encounters a spring after traveling at a speed of 0.57 m/s, compressing the spring and then returning to its starting point. The goal is to determine the total distance the object moves after first touching the spring.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express confusion regarding the known variables and the relationship between kinetic energy, spring potential energy, and work done by friction. There is a discussion about the net work done by the spring and whether all kinetic energy must be accounted for by friction alone.

Discussion Status

The discussion is ongoing, with participants questioning the assumptions made about the work done by the spring and friction. Some guidance has been offered regarding the initial kinetic energy and the forces at play, but there is no explicit consensus on how to proceed.

Contextual Notes

Participants note a potential lack of information and express uncertainty about the implications of the spring's work on the overall energy balance in the system.

dal11
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Homework Statement



An object of mass m=2.2 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.2. The object has speed v=0.57 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. What is the total distance, d, that the object moves after first touching the spring?


Homework Equations



KE+Espring = KEi+Wfriction
Espring=.5k(x^2)
Fspring=kx

The Attempt at a Solution



I am really confused I don't think I have enough knowns to solve the problem.
 
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dal11 said:

Homework Statement



An object of mass m=2.2 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.2. The object has speed v=0.57 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. What is the total distance, d, that the object moves after first touching the spring?


Homework Equations



KE+Espring = KEi+Wfriction
Espring=.5k(x^2)
Fspring=kx

The Attempt at a Solution



I am really confused I don't think I have enough knowns to solve the problem.

I think you may have more information than you realize.

You start with an initial KE at x = 0.

There are two sources of work against the mass from that point.

There is friction and the spring.

But the spring gains potential energy ... but then gives it back until the object it at rest just as it gets to x = 0 again. So how much net work did the spring do?
 
0 I guess, I don't understand how that helps
 
dal11 said:
0 I guess, I don't understand how that helps

If the spring does no net work in stopping the object doesn't all of the kinetic energy of the object need to be accounted for by just the friction over the distance of 2*(d/2) ?

Doesn't mv2/2 = Work of Friction = Ffriction * distance
 

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