Basic Misconception tension in rope and vectors

[rockclimber]

Homework Statement

I am trying to learn enough physics to understand forces in climbing anchors and am stuck with an exercise problem that I am unable to understand my misconception.
Mass-less rope, no friction.

diagrams
https://docs.google.com/drawings/pub?id=1ji6WWzHGx_GwYkb6vneJJCiyjGd8fUAREIR_6HLZbAE&w=960&h=720

Homework Equations

The problem question is diagram D
SB is a spring balance
T1 = 98n, correct
T3 = 98n, correct
SB = 196n, wrong, ( 98n is the correct answer )

The Attempt at a Solution

Isolating each side as in diagram B
T1 = 98n = TB1 = TB2
TB1 force is to the left, TB2 force is to the left so they will not be added together
( from a experimental view I could hold the force exerted 98n )

Putting them back together again as in diagram C
T1 = 98n = T3
TC1 = T1 = 98n
TC2 = T3 = 98n
TC1 + TC2 = 196n
TC1 force is to the left, TC2 force is to the right, so they add together
( from a experimental view I would not attempt the experiment, could be painful )

The tension force in the rope has to be equal in Diagram A
T1 = T2 = T3
but T1 and T3 are downward forces that have to be transmitted somewhere and the only place is T2 so what is T2 ?
T2 = T1 + T3 = 2x98n = 196n
as T1 = T2 = T3 , ( T1 = 98n, T2 = 98n, T3 = 196n, therefore the tension will balance to 392n / 3 = 130n )

Hopefully you can see I have tried to understand but have come to the conclusion that I have a fundamental misconception as regards tension force, could it be something similar to the common mass and weight misconception. ?

 

[kushan]

hey
what is the question asking for

 

[rockclimber]

Why is the spring balance 98n and not 2 x 98n

 

[kushan]

ok rockclimber
I have a question for you
suppose a a spring balance is hung on a wall with the help of a string
and mass m hanging down with the help of a string
what will spring balance show ? reading

 

[rockclimber]

Hi Kushan

98n
or .98 x mass

as isolated in diagram B

I am sure that right

 

[kushan]

So you got the answer ?

 

[rockclimber]

Sorry no

the question is two masses are connected as diagram D

just because the two masses are connected that does not make the force of one of the masses disappear or does it ?

We have two downward forces

Ok, I will try again

One mass hanging has to have a force of 98n, the rope always transmits its tension evenly, therefore it is of no consequence how it is terminated, either by a wall or ( in diagram D ) another mass hanging in opposition .

So one of the forces generated by the mass does not disappear, it is opposed by the other force.

 

[kushan]

Do you find any similarity in this figure and you rquestion ?

in terms of tension aboce the spring and below the spring?

 

[rockclimber]

Yes, the similarity is that the spring is just in a different position,
so the spring will read the same no matter where it is in the system.
Ta = Tb

Is therefore tension force at any point in the rope a pair ( action and reaction ) ( I looked this up ! )
To find the tension in the rope it is either the action force or reaction force of the entire system.

Is the answer to the original question what is the tension, its the reaction force 98n
The spring balance will read 98n because it part of the rope system

Should I be looking more closely at the direction of the arrows in your diagram ?

Thanks

 

[kushan]

Yea and your welcome :)

 

[rockclimber]

Hi Kushan
Many thanks for the help
Wow this is a really friendly place
Cheers
Phil