Tension in a Mass-less String: Explained

[andyrk]

I get that tension in a mass-less string arises because of electrostatic forces which arise because atoms of the string are pulled apart. I also understand that it is equal and opposite in direction at all points because otherwise the string would accelerate infinitely. But what about the last point in the string which is in contact with the block? It has a tension T upwards, but what does it arise because of? Similarly, the topmost point in the string has T downwards. What does it arise because of? And why does it have to be T in both the cases? Can't it be different? If not, why?

 

[pbuk]

By "block" do you mean a static mass hanging from the string or a pulley from which the string is hanging?

If the former, the tension in the string is the equal and opposite reaction to gravity acting on the mass (block).

If the latter, the string is in continuous tension around the pulley (block).

 

[andyrk]

Its the former. Yeah, I get that it is equal and opposite reaction to gravity acting on the mass. But why does it have to be equal to the tension that exists in the rest of the string?

 

[pbuk]

For the same reason that tension is equal at every other point on the string - if it were not, that point of the string would accelerate in the direction of the greater force until equilibrium is reached.

 

[andyrk]

For the same reason that tension is equal at every other point on the string - if it were not, that point of the string would accelerate in the direction of the greater force until equilibrium is reached.

Why would tension at the topmost and bottom most point have to be equal to the tension at the rest of the string? I think that they can be different and still the string won't accelerate.

 

[pbuk]

The downwards force on the bottom of the string is $mg$, so this is the magnitude of the tension at the bottom of the string.

The downwards force on the support at the top of the string is also $mg$, so this is also the magnitude of the tension at the top.

 

[andyrk]

Can you illustrate how this tension equal to $mg$ travels through the entire string?

 

[jtbell]

Mentally divide the string into many short sections.

If a section is stationary, then by Newton's First Law, the net force on it must be zero.

By Newton's Third Law, the force that each section exerts on its neighbor must be equal in magnitude and opposite in direction to the force that the neighbor exerts on it.

Note that in order to make the forces between all pairs of neighboring sections equal, you have to assume that the mass of each section is zero, i.e. the string is massless.

 

[andyrk]

By Newton's Third Law, the force that each section exerts on its neighbor must be equal in magnitude and opposite in direction to the force that the neighbor exerts on it.

But why does each section exert a force on the neighbouring section?

 

[pbuk]

But why does each section exert a force on the neighbouring section?

Because otherwise there would be nothing to stop the end attached to the weight falling to the ground.

 

[jtbell]

But why does each section exert a force on the neighbouring section?

You're basically asking, "why do solids stick together?" Try asking Google that question.

(and then if you need any clarification, by all means ask here...)

 

[andyrk]

If a section is stationary, then by Newton's First Law, the net force on it must be zero.

What do these forces arise because of? Pulling of atoms of the string? I want to know from where does this force originate from?
Also, that means the two forces on a section are equal. Let's call it $T$.

By Newton's Third Law, the force that each section exerts on its neighbor must be equal in magnitude and opposite in direction to the force that the neighbor exerts on it.

Now the sections exert a force on each other. Why does this force have to be equal to $T$?

 

[sophiecentaur]

Now the sections exert a force on each other. Why does this force have to be equal to TT?

If the forces became less than T, the string would stretch / break. If they were more than T the string would be getting shorter.