Heating an aluminum strut in a truss (Feyman Lectures of Physics 2.10)

[new90]

Homework Statement

The truss is made of light aluminium struts pivoted at each end.At C is a roller which rolls on a smooth plste.Whe a workman heats up member AB with a welding torch it is observed to increase in length by an amount x and the load is thereby moved vertically an amount y
A)Is the motion of W upward or downward
B)What is the force F in the member AB (Including the sense i.e.,tension or compression)

Relevant Equations

no equation

A)W goes downward because before AB gets heat up the system was in equilibrium hen after getting heat up the Force that AB produce makes the roller moves to the right and that makes the whole system go down
B)I don't know what it means I know that this can mean the forces that the member Ab is apllying or the forces that are being appliend in member AB(I thnik is the second option)

 

[haruspex]

It would help to know how long you are expected to take solving this.
To do the proper analysis will take some time.

There may be a way to answer A with a simple argument, as you have tried, but I don't find the argument you offer at all convincing. And B will definitely take some equations, so might as well do A that way too.

First step is to identify the parts of the structure which are effectively rigid bodies as AB changes length. This will allow you to represent it with a simpler structure.

 

[Cutter Ketch]

First step is to identify the parts of the structure which are effectively rigid bodies as AB changes length. This will allow you to represent it with a simpler structure.

Listen to @haruspex! Do this. If the lengths of the sides of a triangle do not change neither can their angles. Which triangles change? Which ones stay the same? Color the rigid ones in and see if this doesn’t become more obvious.

 

[Lnewqban]

B)What is the force F in the member AB (Including the sense i.e.,tension or compression)
...
B)I don't know what it means I know that this can mean the forces that the member Ab is apllying or the forces that are being appliend in member AB(I thnik is the second option)

Since the problem shows no numbers or dimensions, the answer to question B can't be a number.
The force within member AB is only one, that aluminum strut can only be tensioned or compressed (pivoted at each end, as stated).

If rather than inducing thermal dilatation with a torch, the workman of our problem would decide cutting off member AB with a hacksaw, would nodes A and B get closer or farther from each other as the structure fails?
What that relative movement would tell you about the type of load or force that the member is "feeling"?

 

[new90]

when you aid fails you means go down right?

 

[new90]

the one colored is the only triangle that change

 

[Lnewqban]

when you aid fails you means go down right?

A structure fails or collapses under load when it stops doing its job.
The job of this structure is preventing the mass W from falling down.
That is not the only possible case, it could be a failing member of a hydraulic press, for example.

 

[Lnewqban]

the one colored is the only triangle that change

Member AB is a common side to two triangles, therefore, at least two must change angles.

 

[Cutter Ketch]

the one colored is the only triangle that changeView attachment 260843

Not quite. If you change the length of AB isn’t it one of the sides of TWO triangles?

 

[new90]

so 4 angles are cheanged

 

[Lnewqban]

so 4 angles are cheanged

Six.
Is our man done cutting that member in half?

 

[new90]

oh yes sorry

 

[haruspex]

oh yes sorry

Call those triangles ABX, ABY. If AB gets longer what happens to the distance XY?

 

[new90]

it increse

 

[Cutter Ketch]

it increse

Hmmm ... I’m not entirely sure what you are saying increases. Do you mean the height of the mass, or one of the angles?

 

[TSny]

it increse

@haruspex asked:

Call those triangles ABX, ABY. If AB gets longer what happens to the distance XY?

 

[Cutter Ketch]

Ahhh ... I see. Thanks, @TSny

 

[Cutter Ketch]

it increse

AY is not changing length. BY is not changing length. Neither are AX or BX. Are you sure than when you separate A and B the distance between X and Y will increase? Suppose you have this contraption made of rigid bars AX, BX, AY, and BY with hinges at all the vertices. AB is a bungee. Imagine going to the extreme. What if you pulled A and B very far apart. What happens to X an Y?

 

[haruspex]

it increse

Model it with your hands. Put your thumb tips together as point X, your fingertips together as point Y, and the joints at the bases of your thumbs as A and B. As you move A and B together and apart, what happens to XY?

 

[new90]

i think what happens is that when is enlongated that X is rater but y decreases

 

[haruspex]

i think what happens is that when is enlongated that X is rater but y decreases

"Rater"? "Greater"?
X and Y are points, they cannot increase or decrease. What happens to the distance XY?

 

[new90]

XY are together ?

 

[haruspex]

Im not sure

Did you try it out with your hands, like I suggested?
As you flex the joints at the bases of your thumbs, when they get further apart do your fingertips get closer to your thumbtips or further away?

 

[new90]

I do that and what I see is that when Y increase X decrease

 

[new90]

I think I will try it tommorrow but thanks

 

[haruspex]

I do that and what I see is that when Y increase X decrease

I'll say it again: X and Y are points. They cannot increase or decrease.

In the hand model, AB is the distance between the joints at the bases of your thumbs, and XY is the distance between your fingertips and your thumbtips.
As you increase the distance between your thumb bases, the distance from your fingertips to your thumbtips decreases, right?

 

[new90]

yes that's what i was trying to say

 

[haruspex]

yes that's what i was trying to say

Ok. So what about the second part?
I assume you know the principle of virtual work.