Spring question, how do I know it is negative or positive?

[flyingpig]

Homework Statement

[PLAIN]http://img33.imageshack.us/img33/8751/49753333t.jpg

Problem #2

[PLAIN]http://img121.imageshack.us/img121/5574/35712633.jpg

My question is, why do they take positive x₀? Shouldn't it be negative since it is that amount of x displacement away from the spring?

 

[Doc Al]

My question is, why do they take positive x₀? Shouldn't it be negative since it is that amount of x displacement away from the spring?

No, x₀ is the distance the spring is compressed.

 

[flyingpig]

No, x₀ is the distance the spring is compressed.

Distance? But why?

 

[Doc Al]

Distance? But why?

Read the problem statement ("...the initial compression x₀...") and look at the diagram.

What would a negative compression mean? A stretching?

If they asked "What is the initial displacement of the spring from its equilibrium position taking 'to the right' as positive?" then you'd give a negative answer.

 

[flyingpig]

Read the problem statement ("...the initial compression x₀...") and look at the diagram.

What would a negative compression mean? A stretching?

If they asked "What is the initial displacement of the spring from its equilibrium position taking 'to the right' as positive?" then you'd give a negative answer.

But the "Initial compression x₀ doesn't really say it is distance or displacement and I thought x in (1/2)kx^2 is always displacement

Also, isn't it always generally taken the right side as the positive and the left side (away from the equilibrium position) is always negative?

Also, even if it is asking for the displacement, what if you take the absolute value? Wouldn't they both work since at the end you will be squaring it again.

 

[Doc Al]

But the "Initial compression x₀ doesn't really say it is distance or displacement

This is more of an English question than a physics question. Seems clear enough to me that "compression" would be a positive number.

and I thought x in (1/2)kx^2 is always displacement

Sure. So?

Also, isn't it always generally taken the right side as the positive and the left side (away from the equilibrium position) is always negative?

If you were asked for the displacement, then that would be the typical convention.

Also, even if it is asking for the displacement, what if you take the absolute value?

I thought you just stated that if they asked for the displacement, the answer would be negative. Taking the absolute value would give you the wrong answer.

Wouldn't they both work since at the end you will be squaring it again.

The value of the spring potential energy is independent of the sign of the displacement. But that doesn't mean that the sign of the displacement makes no difference. (If the displacement were positive--using your convention--that means that the spring was stretched to the right, which would not make sense for this problem.)