Do your weight hang low?

Classical Mechanics Level 3

A weight hangs at a steady height from a rubber band that is attached to the ceiling. Now, you turn on an air conditioner, significantly lowering the temperature of the room. What happens to the position of the weight?

It stays the same It rises It lowers

4 solutions

Andrew Yates
Nov 30, 2015

When you stretch a rubber band it releases thermal energy. Cooling down the room would also release thermal energy from the rubber band, therefor stretching it. Probably the most simplistic explanation, but those are sometimes the best!

Anandhu Raj
May 11, 2015

Most materials expands on heating, while but when an elastomer is assumed to be in a stretched state, heating causes them to contract. Vice versa, cooling can cause expansion .This can be explained by Gibb's Free Energy .

Yes, you are right. This is a beautiful question.

A lot of thermodynamic properties are associated with a rubber band based on its structure. If you quickly stretch the rubber band and then press it against your lips, you will feel a slight warming effect. Now reverse the process. Stretch a rubber band and hold it in position for a few seconds. Then quickly release the tension and press the rubber band against your lips. This time you will feel a slight cooling effect. A thermodynamic analysis of these two experiments, gives us a good insight of molecular structure of rubber.

Raghav Vaidyanathan - 6 years, 1 month ago

Well, this is what I have to say: since cooling down the air in the room would make it more dense, so the buoyant force on the weight will increase, rising it up. While it is quite obvious that the the effect due to that would usually be much lesser than what you have mentioned, I suggest you should add some assumption to the question so that others don't make the same mistake as I did.

Aalap Shah - 6 years, 1 month ago

One query.. At room temp, will humidity be a major factor in expansion of the string since humidity also makes the air more dense albeit the string is present in room temperature ?

Parag Zode - 6 years, 1 month ago

Think again.....I think dry air is more denser than humid air. Also the effect of buoyancy is negligible.

Anandhu Raj - 6 years, 1 month ago

@Anandhu Raj – Agreed! Humidity is water vapour not liquid water and thus the weight of molecules is lighter as compared to weight of molecules in one glass of water. But will the atmospheric pressure of the dry air be more than that of humid air ?

Parag Zode - 6 years, 1 month ago

@Parag Zode – Atmospheric pressure won't affect the question because it acts in all directions equally and cancel out. I think you are referring to the effect of buoyancy.If then buoyancy only depends on density of surrounding medium and not pressure.

Also weight of (water)molecules is constant irrespective of whether they are in liquid or vapour state.Dry air is more denser because in unit volume dry air has more concentration of heavier molecules(oxygen, nitrogen, carbon dioxide, etc..) than lighter water molecules.

Atmospheric pressure changes negligibly because the pressure increase due to addition of water molecules is compensated by decrease in the number of dry air molecules unless any restriction is done to prevent this.

Anandhu Raj - 6 years, 1 month ago

@Anandhu Raj – 1st point agreed. But, weight of water molecules is not constant. In fact, the weight of water molecules is more in liquid state than in vapour state. See this link:- www.washingtonpost.com/blogs/capital-weather-gang/wp/2013/08/05/why-dry-air-is-heavier-than-humid-air/

Sorry for not attaching a direct link as I don't know how to program a link in a comment...

Parag Zode - 6 years, 1 month ago

@Parag Zode – I doesn't say water molecules are heavier but seems to be heavier.

PS: To attach a link in comment use " $[word ](URL)$ "

Anandhu Raj - 6 years, 1 month ago

Rubber has an unusual molecular structure. The long chain molecules (polymers) actually become shorter at higher temperature as they vibrate more. (Hang a rope from your hand so that it touches the floor. Vibrate it and it lifts from the floor.) So when colder the rubber molecules actually become longer.

John Mcquistan - 3 years, 9 months ago

The spring constant of a rubber band increases as temperature goes down until it reaches the glass transition temperature when it stops being a rubbery material and becomes rigid. So, at a lower temperature more force is needed to stretch the rubber a given length. This answer does not agree with this fact.

Julián López - 5 years, 6 months ago

Fredric Suresh
May 11, 2015

I found this explanation interesting http://www.physlink.com/Education/AskExperts/ae573.cfm

i think rubber band will rise up because on cooling the thermal velocities of rubber molecules decreases due to which they comes closer and as the result it will compress and rise up and vise-versa

Sarvesh Shukla - 6 years, 1 month ago

Zen When the air cools it becomes denser so the upthrust is more Arc. pr. So the object rises

Marie Silvestri - 5 years, 6 months ago

The suggestions and comments here seem to be contradictory. Has anyone actually done this?

David Hobday - 3 years, 10 months ago

It doesn't look like very difficult to do at home. Maybe I'll try it if I find the time. My bet is that the weight will go up but one never knows...

Félix Pérez Haoñie - 2 years, 6 months ago

Bullshit. It will rise.

John McMurtry - 3 years, 6 months ago

Xiaofei Tian
Jun 3, 2017

entropic spring

Do your weight hang low?

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