# Spring question, theory and a simple application.

## Homework Statement

The stopping distance of a 0.40 kg weight which slides into a spring with k = 750 N/m at a speed of 1/2 m/s is 0.012 metres. Can we now calculate the original uncompressed length of the spring from this info?

## The Attempt at a Solution

m = 0.4kg
k = 750N/m
v = 0.5m/s
x_final = -0.012m
x_initial = ?

My main concern is this

Should I assume the initial spring position is x_initial = 0? Can you pull the spring and stretch it like the picture?

[PLAIN]http://img200.imageshack.us/img200/1659/unledjp.jpg [Broken]

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## Answers and Replies

kuruman
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To answer your second question first, yes you can stretch the spring as you show. At 0.012 m stretch the magnitude of the force exerted by the spring will be the same as at 0.012 m compression.

For the first question, yes you can assume that x=0 at the unstretched position (red line) in your drawing. The 0.012 m compression point is to the left of the line. You are looking for the distance to the black line in your drawing. Do you think you can find it with the information given?

Here is a related question. Can you have two springs that have different uncompressed lengths but the same spring constant?

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Sure, spring constants are constants it shouldn't be anything related to the natural lengths of the spring.

But how do we know that x_initial isn't 0.012m?

kuruman
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How do you define x_initial? It is the distance from where to where in your drawing? You have a line at "x=0". Is that where the end of the spring is before the mass hits it?

I thought x_initial is always measured from the equilibrium point.

kuruman
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I thought x_initial is always measured from the equilibrium point.
You are correct. What does "equilibrium" mean as far as the spring being stretched or compressed?

It's the point where the spring wants to be at msot.

kuruman
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I don't understand what "msot" means. Can you explain?

*most

*at the most.

You can tell I didn't do well in my English class

kuruman
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You define the equilibrium position as the position where the spring "wants to be at the most." Most what?

It wants to stay at the equilibrium point.

kuruman
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So, you are saying that the equilibrium point is where the spring "wants to stay." Springs don't "want" things like you and I want things. Can you come up with a better definition? Perhaps do some search on the web? You should be able to answer your own question with a better definition for equilibrium. If not, show us the definition you found and we will explain it to you and how it applies to your question.