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How to determine the direction on tension

I'm doing M1 atm and I come across so many tension questions everywhere everyday, but sometimes I determine the direction of tension wrong, is there like a thought process you go through to determine which way tension is pointing? Thanks this is one my key issues with the dynamics chapter

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Reply 1

Indeterminate

Original post by Robbie242

Tension is the "stretching" force (i.e it creates tension), so is always in the direction that would stretch a string or something.

You must have heard of the saying "you could cut the tension with a knife" :biggrin:

(edited 11 years ago)

Reply 2

Robbie242

Original post by Indeterminate

Tension is the "stretching" force (i.e it creates tension), so is always in the direction that would stretch a string or something.

So say on this question Two particles P and Q, of mass 4kg and 6kg respectively, are joined by a light inextensible string. Inititally they are at rest on a rough hortizontal plane with the string taut.

First of all would there be two tensions?
and secondly would the tension from p be -> inbetween particles P and Q whilst for Q it would also be -> I don't know, I'm really bad at this

Reply 3

Indeterminate

Original post by Robbie242

There are two tension forces.

Hint:

To make a string taut ("stiff") in your hands, you'd pull it out in both directions as far as possible, right?

Reply 4

Robbie242

Original post by Indeterminate

There are two tension forces.

Hint:

To make a string taut ("stiff") in your hands, you'd pull it out in both directions as far as possible, right?

Oh that really helps, so would it be say Particle P-<------>---Q is what your saying right?
if it is, I hope I don't get in trouble for doing that in the exam haha i.e moving my hands apart in mid-air :P

(edited 11 years ago)

Reply 5

Indeterminate

Original post by Robbie242

Oh that really helps, so would it be say Particle P-<------>---Q is what your saying right?

they act in the direction that's inwards (i.e towards the centre of the string) :smile:

(edited 11 years ago)

Reply 6

Robbie242

Original post by Indeterminate

Yes, they act in the direction that's outwards from the centre of the string :smile:

are there special cases where the concept of tension is slightly different?, i.e. what if its string holding an object below the pulley, would 1 tension force be acting upwards, as the weight would be stretching it downwards?

(edited 11 years ago)

Reply 7

.raiden.

Original post by Robbie242

The pulley pulls on the particle as you assume that the pulley is fixed, that's how i like to think of it makes sense in a way

Reply 8

.raiden.

Original post by Indeterminate

You would still have 2 tensions, but resolving (in equilibrium) would give

T - mg = 0 \Rightarrow T=mg

so they would cancel each other out.

Note also that, if a string is slack ("loose"), then there is no tension.

What is the special name given when the arrows are facing out instead of in? I can't remember the name

Reply 9

Indeterminate

Original post by Robbie242

resolving (in equilibrium) would give

so they would cancel each other out.

Note also that, if a string is slack ("loose"), then there is no tension.

(edited 11 years ago)

Reply 10

Robbie242

and would it be correct saying one is acting up and the other one down? by saying they cancel out do you mean the same effect, so you count it as one, because surely mg cannot equal 0 since a block must have some sort of degree of mass

Original post by Indeterminate

You would still have 2 tensions, but resolving (in equilibrium) would give

so they would cancel each other out.

Note also that, if a string is slack ("loose"), then there is no tension.

Cheers btw

(edited 11 years ago)

Reply 11

.raiden.

Original post by Robbie242

The resultant force is zero, T is the same force as the weight (mg) acting in opposite direction

(edited 11 years ago)

Reply 12

Indeterminate

Original post by Robbie242

Sorry, I should've been more clear. You needn't think of it as two tensions. Instead, think of it as T cancelling out mg (in equilibrium)

Reply 13

Robbie242

Original post by Indeterminate

Sorry, I should've been more clear. You needn't think of it as two tensions. Instead, think of it as T cancelling out mg (in equilibrium)

Cheers, yeah so when an objects hanging down and I resolve upwards, tension will be positive and downward forces negative, ty

Reply 14

RoyalBlue7

Original post by Indeterminate

Yes, they act in the direction that's outwards from the centre of the string :smile:

I think this is all wrong!

Tension acts along the string, but in M1 we don't consider the string! We only consider the free body diagram of the particles and not the string, i.e. the forces that act on the particle and not the string. In this context the tension will be the force by which the string pulls the particles (when it is taut) and that will be along the line of the string. Therefore P and Q both will both experience a tension force exerted by the string that tries to draw both towards each other.
If a taut string is involved with a pulley or beads etc the tension force along it will be the same in magnitude if the pulley etc is smooth.

As tension is the magnitude of a force, it is measured in newtons (or sometimes pounds-force) and is always measured parallel to the string on which it applies

Tension forces can be modeled using ideal strings which are massless, frictionless, unbreakable, and unstretchable. They can be combined with ideal pulleys which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object.

(edited 11 years ago)

Reply 15

Indeterminate

Original post by StUdEnTIGCSE

No, the tension would only pull in in towards the centre of the string if the two particles are on an inclined plane. This stops the particle that's lowest from falling away.

On a horizontal surface, the particles "hold on" to the string to keep it taut and stop it from "relaxing", so tension pulls away from the centre.

Reply 16

RoyalBlue7

Original post by Indeterminate

On a horizontal surface, the particles "hold on" to the string to keep it taut and stop it from "relaxing", so tension pulls away from the center.

Yes but we don't consider the string! We consider the particles.
We only consider the Newton Third Law pair of that, the tension force exerted by the string on the particles!

eg; Particle P pulls the string away from its center of mass with a tension force of x magnitude
So the string pulls P towards its center with a tension force of x magnitude.