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.
The direction of the spring's movement or displacement is what determines if it is positive or negative. If the spring is moving towards its equilibrium position, it is positive. If it is moving away from its equilibrium position, it is negative.
Yes, a spring question can have both positive and negative values. This depends on the direction of the displacement of the spring. It is important to designate a reference point or equilibrium position to determine if the values are positive or negative.
The direction of a spring's displacement can be measured using a coordinate system. This can be a simple number line or a more complex Cartesian coordinate system. The positive and negative values can be assigned to the direction of the displacement based on the chosen reference point.
Knowing the direction of a spring's displacement, or whether it is positive or negative, is important for understanding its behavior and mathematical equations. It also helps in determining the forces acting on the spring and predicting its motion.
Yes, a spring question can have a zero value. This means that the spring is at its equilibrium position and is not experiencing any displacement. In this case, the direction of the displacement is neither positive nor negative.