A pulley system with two pulleys and two suspended masses

[erobz]

Which two equations sorry?

Many thanks!

The first one we derived with that one. they both equal $L$. You are attempting to figure out how the changes in each variable relate to each other.

 

[ChiralSuperfields]

The first one we derived with that one. they both equal $L$.

Thank you for your reply @erobz !

That must be $L = a + 2s + 2b + l$ and $L = a + 2s + \Delta 2s+ 2b + l + \Delta l$

So
$a + 2s + 2b + l = a + 2s + \Delta 2s+ 2b + l + \Delta l$
$0 = \Delta 2s + \Delta l$
$-\Delta 2s = \Delta l$
$2(s_f - s_i) = l_f - l_i$
Many thanks!

 

[erobz]

Thank you for your reply @erobz !

That must be $L = a + 2s + 2b + l$ and $L = a + 2s + \Delta 2s+ 2b + l + \Delta l$

So
$a + 2s + 2b + l = a + 2s + \Delta 2s+ 2b + l + \Delta l$
$0 = \Delta 2s + \Delta l$

Many thanks!

Move one of them to the other side of the zero. And if you want to know how far pulley B moves in terms of a how far pulley A moves solve for $\Delta s$.

 

[erobz]

Again. Keep the $\Delta$ touching the $s$. They are stuck together. Joined at the hip! don't put that 2 in between them.

 

[ChiralSuperfields]

Again. Keep the $\Delta$ touching the $s$. They are stuck together. Joined at the hip! don't put that 2 in between them.

Thank you for your reply!

Sorry @erobz missed that message,

$-2\Delta s = \Delta l$

Many thanks!

 

[ChiralSuperfields]

Thank you for your help @erobz !

Just a side question, how were we allowed to add the $\Delta$ to $s$ and $l$ then set them equal to each other?

Many thanks!

 

[erobz]

Thank you for your help @erobz !

Just a side question, how were we allowed to add the $\Delta$ to $s$ and $l$ then set them equal to each other?

Many thanks!

Because the change is unsigned. It could be a positive change. It could be a negative change. It may appear like were adding to both lengths but is turns out we weren't. Notice the equation dictates a positive change in the variable $l$ ( $\Delta l > 0$) demands and negative change in $s$ ( $\Delta s < 0$), and visa-versa.

 

[ChiralSuperfields]

Because the change is unsigned. It could be a positive change. It could be a negative change. It may appear like were adding to both lengths but is turns out we weren't. Notice the equation dictates a positive change in the variable $l$ ( $\Delta l > 0$) demands and negative change in $s$ ( $\Delta s < 0$), and visa-versa.

Thank you for your reply @erobz !

I think we can only add the $\Delta$ to the variable that is changing if know that there is a constraint for example the string length is conserved, correct?

Many thanks!

 

[erobz]

Thank you for your reply @erobz !

I think we can only add the $\Delta$ to the variable that is changing if know that there is a constraint for example the string length is conserved, correct?

Many thanks!

No. You can add it to anything. The only constraint needed is that you have a relationship between some variables. It's simply saying we have this relationship between all these variables, lets pick some or, all that can change and change them a bit from where they currently are valued at, and see how they respond to each other. How it all pans out or the end goal is specific to each situation.

The main motivation is derivatives and differential equations, where you are looking for the change in one variable w.r.t a change in another variable. You've got time to learn all this. You don't have to figure all this out yesterday.

 

[ChiralSuperfields]

No. You can add it to anything. The only constraint needed is that you have a relationship between some variables. It's simply saying we have this relationship between all these variables, lets pick some or, all that can change and change them a bit from where they currently are valued at, and see how they respond to each other. How it all pans out or the end goal is specific to each situation.

The main motivation is derivatives and differential equations, where you are looking for the change in one variable w.r.t a change in another variable. You've got time to learn all this. You don't have to figure all this out yesterday.

Thank you for your help @erobz ! :)

 

[haruspex]

$L = a + 2\Delta s + 2b + \Delta l$

No, the deltas are the increases in length. The original lengths should still be in the equation. You should have just replaced $s$ with $s+\Delta s$, etc.

 

[BvU]

I am somewhat flabbergasted at the length () of this thread!
If you do the experiment with a real piece of rope things will be clear quickly.

If you still insist on a mental exercise, remove all unessentials: reduce the pulleys to points, etc

$\$

 

[erobz]

No, the deltas are the increases in length. The original lengths should still be in the equation. You should have just replaced $s$ with $s+\Delta s$, etc.

It was getting late! I guess my mind was just inserting symbols that weren’t there.

Edit: Actually at a later post (#31) than what you must have been quoting they did get the proper result.

 

[Lnewqban]

However, how do they know the block B will move up and block A will move down?
...
Also how do they know that if block B moves up by 1cm, block A will move down by 2cm?

Do you now understand how do they know those things?

If not, please see:
https://www.physicsforums.com/threa...2-dynamics-problem-involving-a-pulley.991370/

 

[ChiralSuperfields]

No, the deltas are the increases in length. The original lengths should still be in the equation. You should have just replaced $s$ with $s+\Delta s$, etc.

Thank you for your reply @haruspex ! I will try that sometime.

Many thanks!

 

[ChiralSuperfields]

I am somewhat flabbergasted at the length () of this thread!
If you do the experiment with a real piece of rope things will be clear quickly.

If you still insist on a mental exercise, remove all unessentials: reduce the pulleys to points, etc

$\$

Thank you for your reply @BvU!

Sorry, what do you mean reduce the pulley to points?

Many thanks!

 

[ChiralSuperfields]

It was getting late! I guess my mind was just inserting symbols that weren’t there.

Edit: Actually at a later post (#31) than what you must have been quoting they did get the proper result.

Thank you for your reply @erobz !

 

[ChiralSuperfields]

Do you now understand how do they know those things?

If not, please see:
https://www.physicsforums.com/threa...2-dynamics-problem-involving-a-pulley.991370/

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Thank you for sharing that thread @Lnewqban !

 

[BvU]

Sorry, what do you mean reduce the pulley to points?

You can get far with just a few pins or paperclips and a piece of wire, real or imagined ..

$\$

 

[ChiralSuperfields]

You can get far with just a few pins or paperclips and a piece of wire, real or imagined ..

$\$

Ok thank you @BvU !