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Slinky Free Fall

Last updated on July 13th, 2020 at 09:15 pm

One evening recently, I and my friends were hanging out in a park. We were having a discussion over something and it was then suddenly,

My Friend: ” Hey! Do you believe that there are certain concepts we study during our childhood but fail to apply it in our day to day life? “

Me: ” Oh C’mon! I am pretty confident about what I have studied till now. “

My Friend: “Let’s see if you can explain the behavior of a slinky (a toy) in its free fall.”

Me (confidently): ” It will free fall under gravity. What’s a great deal in it.”

After that, he had a huge laugh at me and told me about the Slinky Free-Fall Experiment. The illustration is as follows:

Try it yourself if you don’t agree to it. What do you observe?

To my surprise, even I was shocked how could I miss such a simple concept from school. Well, many of you must be aware of this but if not here is the explanation to this experiment and property of a spring.

Explanation

One key to understanding this is the following fact from classical mechanics that is a version of Newton’s second law for systems of particles:

The net external force acting on a system of particles equals the total mass M of the system times the acceleration of its center of mass

F(ext,net)=Ma(COM)

In the case of the slinky, which we can model as a system of many particles, the net external force on the system is simply the weight of the slinky. This is just given by its mass multiplied by g, the acceleration due to gravity, so from the statement above, we get

Mg=Ma(COM)

so it follows that

a(COM)=g

In other words, we have shown that

The center of mass of the slinky must move as if it is a particle falling under the influence of gravity.

However, there is nothing requiring that the individual particles in the system must move as though they are each falling freely under influence of gravity. This is the case because there are interactions between the particles that affect their motion in addition to the force due to gravity.

Take look at this part of the slinky

enter image description here

On the part above, there are three forces acting on it. The tension from the upper part of the slinky, the tension from the lower part of the slinky and mg. All of them are balanced.

But if you talk about this part of the slinky:

enter image description here

The forces are Tension, mg and that force by the hand. Note that mg and tension are in the same direction i.e downwards and they are balanced too, obviously.

When you release the slinky, the net force on the topmost element becomes tension+mg and is pointed downward but on the rest of all the parts of the slinky, the forces are STILL balanced.

So what you see is the topmost part rushing down while the others just stay in their position.

NOTE – It is the property of the spring that the spring force or spring tension does change immediately.

Video Courtesy- ” Veritasium ”

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Abhijeet is a 4th-year Undergraduate Student at IIT Kharagpur. His major inclination is towards exploring the science behind the things of our day-to-day life.

Abhijeet Mahatohttp://scilynk.in
Abhijeet is a 4th-year Undergraduate Student at IIT Kharagpur. His major inclination is towards exploring the science behind the things of our day-to-day life.

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