How to take into account Force when comparing two lengths?

[Sagar Bhatt]

The attached picture sums up my experiment. I used a slinky (a kind of a bouncing spring) to see the relationship between its maximum length when released and the length of its first rebound. However, I released the slinky using various different magnitudes of force. I used a sensor (a LabQuest 2) so I know the position, velocity and acceleration of the slinky for all my data points at all times. I'm guessing the force would equal mass of the slinky times acceleration at time 0 for each data point. But how would I put that into consider in my experiment? It does need to be considered. I want to make calculations such that both lengths reflect what would happen if the slinky was dropped at a constant force for all data points.

 

[Simon Bridge]

Please detail the experiment - what are you doing step by step?
The diagram suggests you throw it from a height.

i.e. Are you holding one end some distance above the floor so the other end touches the floor, then releasing that end?

 

[brotherStefan]

I'm not sure I understand your procedure or objective. Is the Slinky initially suspended from a fixed stand? Before you stretch the Slinky, are its coils fully compressed? Are you trying to determine how much energy is lost in the rebound?

 

[Sagar Bhatt]

what are you doing step by step?

1. I'm taking a slinky and releasing it from three different heights above the LabQuest sensor.
2. (The height doesn't matter here, the slinky's initial length when released and the length of the subsequent rebound do.)
3. (The height's only changed because sometimes the slinky gets too long and it crashes into the sensor, which it musn't, and at other times gets too short and thus it's too far away from the sensor to be detected.)
4. The sensor collects data (time, position (m), velocity (m/s), acceleration (m/s^2)) for 5 seconds, though really all the information I need is collected within the first 2 seconds.

i.e. Are you holding one end some distance above the floor so the other end touches the floor, then releasing that end?

It doesn't touch the floor, it's left suspended above the sensor. I do measure the distance from the top of the sensor to the slinky's bottom (when it's stationary). I only release the slinky once, and then observe it bouncing down and then rebounding.

 

[Sagar Bhatt]

Is the Slinky initially suspended from a fixed stand?

It's suspended from three fixed heights. As I said in the reply before, the height doesn't matter here, the slinky's initial length when released and the length of the subsequent rebound do. The height's only changed because sometimes the slinky gets too long and it crashes into the sensor, which it musn't, and at other times gets too short and thus it's too far away from the sensor to be detected.

Before you stretch the Slinky, are its coils fully compressed?

Yes, the coils are fully compressed before it is released.

Are you trying to determine how much energy is lost in the rebound?

I'm not trying to determine how much energy's lost in the rebound. I'm trying to measure the relationship between the maximum length of the slinky when it first bounces to the length of the first rebound.

 

[Sagar Bhatt]

I just made a new diagram to be clearer. Really need the help

 

[Simon Bridge]

When you say you are releasing the slinky and it rebounds, I am picturing you holding the slinky at the top end, then ;letting go of the top end so the entire slinky falls. If so then how do you control the length before it drops? i.e.
http://blogs.discovermagazine.com/badastronomy/2011/09/26/slinky-drop-physics/#.VtTaGrJ97VM

But maybe you mean that the slinky is fixed at the top, you stretch it from the bottom and let the bottom end go so that end bobs up and down? So it is a mass-on-spring experiment without a physical weight on the end? (This is what the plots appear to show.)

If so then: for what purpose do you need to account for the different force needed to produce the different lengths? Unless you push or pull a bit more on the end when you let it go?
Otherwise - No - the force on the slinky is not it's mass of the slinky times the acceleration of the end because different parts are under different accelerations. You need to model the slinky as a massless spring with a mass on the end of it ... you can do some tests to find out if the slinky obey's hook's law first.
But you also need to know why you are doing it.

It is usually easier to understand this sort of result in terms of energy changes.