Mass compressing an unattached spring

• JJ__
In summary, the behavior of the spring and block in this scenario depends on various factors such as mass, friction, and the model used to analyze it. If the spring is attached to the ramp, it may extend beyond its natural length and slide up the ramp from its original position. However, if the spring has no mass, it will simply return to its original unloaded length and the block will lose contact again. If the spring has mass, it will continue to stretch and move past its original position until gravity stops it. The block may separate at the same point, depending on the speed and friction. The vibration of the spring may also affect the behavior of the system.
JJ__
How far will the spring extend, given that the block is not attached? Will it extend beyond its natural length? How to calculate at what point the box comes off the spring?

I think it could - extend beyond its unloaded length and, if the spring is not attached to the ramp, slide up the ramp from its original position.
Exactly what happens will depend on the details; the mass of the spring, friction between the spring and the ramp and between the block and the ramp.
Simple questions (or should I say, questions based on a simple model) treat a spring as an ideal store of energy with a well-defined, linear force-extension relation. Once you start modelling taking account of mass and losses, it gets mathematically more difficult.
If the spring has no mass, hence no momentum, it simply returns to its original unloaded length and the block loses contact again at that point. If it has mass then it is obviously moving at that point, so will continue to stretch (the parts of the spring are moving at different speeds) and will also move bodily past that point until gravity stops it.
My intuition is that the block is then at its fastest, as the spring is now slowing down and using its KE to stretch itself. In which case the block may separate at exactly the same point. If there's enough friction, the block may not separate at all - like a critically or over damped oscillation of a spring-mass system.
But I haven't done any maths on it to check any of that.

256bits and anorlunda
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wall spring mass

Let t_0 be the time when the spring has compressed the most. If everything is standing still at that moment and the spring is lossless, then flip the direction of the time at t_0 and play the history backwards. The mass bounces back and the spring is left static.

However, the speed of sound cannot be infinite in a spring. Some kinetic energy of the mass is converted to vibration of the spring. Everything is not standing still at the time t_0.

It would be a miracle if the mass would absorb all that vibration by the time it detaches from the spring.

The vibration will cause the spring to bounce from the wall and follow the mass.

256bits and hutchphd

1. What is mass compressing an unattached spring?

Mass compressing an unattached spring refers to the process of applying a force to a spring without attaching it to any other object. This results in the spring being compressed or shortened.

2. How does mass affect the compression of an unattached spring?

The mass of an object does not directly affect the compression of an unattached spring. However, the force applied to the spring will determine how much it compresses. The greater the force, the more the spring will compress.

3. What is the relationship between force and compression in an unattached spring?

The relationship between force and compression in an unattached spring is described by Hooke's Law, which states that the force applied to a spring is directly proportional to its displacement or compression.

4. How does the stiffness of a spring affect its compression when mass is applied?

The stiffness of a spring, also known as its spring constant, determines how much force is needed to compress the spring a certain distance. A stiffer spring will require more force to compress compared to a less stiff spring.

5. What factors can affect the compression of an unattached spring?

The compression of an unattached spring can be affected by several factors, including the force applied, the stiffness of the spring, the mass of the object, and any external forces acting on the spring. Temperature and material properties of the spring can also play a role.

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