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I have the following setup: Tightening a string

The string of negligible mass, causing little friction, is shown in dark blue and is fixed at the red circle. The taut string is shown in light blue (with excess string removed). I have shown an orange arrow which indicates the direction in which the string is being pulled. Importantly the force is always exerted at that location and any excess string is removed.

I would like to know how the string deforms over time as it is pulled from that point (orange). Does the end closest to the pulling force move first and straighten up, wrapping around the object 'A' early on, or does the whole string change shape continuously?

How does the direction of pulling force affect things if at all?

Thanks in advance.

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is gravity perpendicular to the plane? –  anna v Mar 29 at 11:50
    
If there is no friction, when you start pulling the string, you give it kinetic energy. Without friction to dissipate that energy, it starts moving and never stops. You will thus need to solve a differential equation which I don't know enough physics to write down, but it will depend on parameters you haven't given us like the elasticity of the string. –  Peter Shor Mar 29 at 13:15
    
Sorry Anna, I definitely should have specified that. Yes, gravity is perpendicular to the plane, so this is essentially a birds-eye view. I am particularly interested about what the situation would be for someone pulling say, thin, flexible, light yarn thread, with their hand, with the thread lying on a marble surface for example. I gave this a go practically and it seemed like my idea was what happened, but I was left unsure as to what happens to the string over a short time period dt. –  user1585968 Mar 29 at 14:02

2 Answers 2

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I would like to know how the string deforms over time as it is pulled from that point (orange). Does the end closest to the pulling force move first and straighten up, wrapping around the object 'A' early on, or does the whole string change shape continuously?

For a better understanding,

Take a look at this figure( I've modified the diagram in order to explain things in a better way )

enter image description here

When the string is pulled, the coil of wire( initially slack ) as shown in region $B$ begins to uncoil. What you will observe is that the portion of the wire in region $A$ begins to move only after the coil of wire in region $B$ gets completely uncoiled( it remains slack until then ). Try it out with a thread or a chain. This is to show you that the portion of the wire close to the pulling force will move first followed by the other portions of the wire.

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The behavior you describe is fairly typical if the string is lying on the ground, so that there's significant static friction resisting its movement. If the string is in free-fall, or, say, floating on/in water, things can be very different. –  Ilmari Karonen Mar 29 at 17:06
    
Thanks a lot. I think the scenario you describe suits my purposes well. –  user1585968 Mar 30 at 11:21
    
@Ilmari Karonen, anna v has given a very good explanation about how atoms that make up the string transmit forces. One cannot expect all the atoms to experience a force at an instant the external force is applied. As anna v said, there will be an impulse propagating through the string starting from the left. –  R004 Mar 30 at 15:46

While it is slack it will depend on the type of string and the transmission of forces. There will be an impulse propagating across the string starting from the left , there might be rotational energy while it is slack. Think of the molecules composing the string, they transmit the force to their neighbor.

Once it tightens it will depend on the actual geometry. In your drawing it will meet A before all the slack is taken so some frictional force will enter.

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Very well explained. –  R004 Mar 30 at 15:24

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