How Does Friction Affect the Speed of a Block Hitting a Spring?

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Homework Help Overview

The problem involves a block colliding with a spring, where the effects of friction on the block's speed are being analyzed. The context includes concepts from mechanics, specifically energy conservation and the work-energy principle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between kinetic energy and the work done by friction, questioning how energy is transformed and dissipated during the collision with the spring. There are attempts to connect the equations for work done by friction, kinetic energy, and spring potential energy.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of energy transformation and the equations involved. Some guidance has been offered regarding the relationship between kinetic energy and friction, but no consensus has been reached on how to derive the speed of the block.

Contextual Notes

Participants are navigating the complexities of energy conservation in the presence of friction, with specific values and parameters provided in the original problem statement. There is an emphasis on understanding the interplay between different forms of energy and forces involved.

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Homework Statement



A moving 1.3 kg block collides with a horizontal spring whose spring constant is 491 N/m.The block compresses the spring a maximum distance of 5.0 cm from its rest postion. The coefficient of kinetic friction between the block and the horizontal surface is 0.49.What is the speed of the block when it hits the spring?

Homework Equations


W_spring=1/2kx^2
KE=1/2mv^2

The Attempt at a Solution


I do not understand how to calculate the blocks velocity. Can someone help me out with this one?
 
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There is one more equation, having to do with the work done by friction.

Think energy:

What happens to the KE of the moving block? (Where does it "go"?)
 
Does the kinetic energy go against the friction force. So would it be F_fric=U_k*mgd?
 
Last edited:
energy is energy, force is force. Energy doesn't "go against" force.

The work done by friction, is [tex]F_f d[/tex]

And that is what I think you have written: [tex]W_f = \mu mgd[/tex]

When the spring is at full compression, how much KE has been "lost"? Some of it has transformed (conserved as mechanical energy) and some has been dissipated (as heat). All energy has to be accounted for.

3 equations, put them together.
 
W_f=umgd
KE=1/2mv^2
W_spring=1/2kx^2

How do you relate these three equations to get a speed? That is what I am struggling with.
 

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