Yes, I triedBvU said:
I think @BvU's point is that we need to see it!Differentiate it said:
So, that would be correct for a particle, why do you think it doesn't work for a spring?Differentiate it said:
To add to what @bob012345 is hinting at, specifically think about the fixed end. What velocity is it moving at?bob012345 said:
Not suddenly, I think. That would get you into complexities of internal oscillations.bob012345 said:
I looked at this problem as idealized. The free end of an unstretched spring is found to be moving at velocity ##v##. Suddenly was an unfortunate choice not because of what the actual dynamics of a real spring would be since this is an ideal spring, but because there is no need to involve time at all. This is a snapshot.haruspex said:
An ideal spring is massless; this one isn't, which is why a sudden tug will likely induce internal oscillations.bob012345 said:
Sure, but for this problem there is only an agent pulling the free end with uniform velocity. It must be assumed that there is also a velocity distribution set up along the spring and we don't need to worry about the details of how that came about.haruspex said:
Quite so, we have to assume some sort of steady state, whatever that means in this context. Hence, no sudden movements.bob012345 said:
@Differentiate it, have you used the hints we gave you to make progress with this problem?Differentiate it said:
The formula for calculating the kinetic energy of a spring is:
KE = 1/2 * k * x^2, where KE is the kinetic energy, k is the spring constant, and x is the displacement from the equilibrium position.
The mass of an object does not directly affect the kinetic energy of a spring. The kinetic energy of a spring is determined by the spring constant and the displacement from the equilibrium position.
The potential energy and kinetic energy of a spring are interrelated. As the potential energy of a spring increases, the kinetic energy decreases, and vice versa. This is because the total energy of the system (spring and object) remains constant.
Yes, the kinetic energy of a spring can be negative. This means that the object attached to the spring is moving in the opposite direction of the spring's displacement. However, the total energy of the system (spring and object) will still remain constant.
The spring constant has a direct effect on the kinetic energy of a spring. A higher spring constant means that the spring is stiffer, and therefore, the object attached to it will have a greater kinetic energy when displaced. On the other hand, a lower spring constant will result in a lower kinetic energy for the object.