The discussion revolves around the interpretation of displacement and compression in the context of a spring problem. Participants are examining why the initial compression, denoted as x0, is considered positive and the implications of this choice in relation to the spring's equilibrium position.
The conversation is ongoing, with participants providing insights into the definitions of compression and displacement. There are differing views on the implications of sign conventions and how they relate to the physical setup of the problem.
There is a focus on the language used in the problem statement and how it influences the interpretation of the spring's behavior. Participants are considering the conventional directions for positive and negative displacements in relation to the spring's equilibrium position.
No, x0 is the distance the spring is compressed.flyingpig said: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 said:No, x0 is the distance the spring is compressed.
Read the problem statement ("...the initial compression x0...") and look at the diagram.flyingpig said:Distance? But why?
Doc Al said: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.
This is more of an English question than a physics question. Seems clear enough to me that "compression" would be a positive number.flyingpig said:But the "Initial compression x0 doesn't really say it is distance or displacement
Sure. So?and I thought x in (1/2)kx^2 is always displacement
If you were asked for the displacement, then that would be the typical convention.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?
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.Also, even if it is asking for the displacement, what if you take the absolute value?
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.)Wouldn't they both work since at the end you will be squaring it again.