Wheels linked by belts: find the one with the least rate of rotation

[Confused101]

Homework Statement

See Diagram

Homework Equations

See Diagram

The Attempt at a Solution

I have been looking for hours for the correct formula but do not know what to use or where to start. If you can point me in the direction of the right formula if one is needed, and I would be very grateful. Is it something to do with velocity ratios ? Thanks

 

[SammyS]

View attachment 83344

Homework Statement

See Diagram

Homework Equations

See Diagram

The Attempt at a Solution

I have been looking for hours for the correct formula but do not know what to use or where to start. If you can point me in the direction of the right formula if one is needed, and I would be very grateful. Is it something to do with velocity ratios ? Thanks

Physics is much less about finding formulas than it is about analyzing a situation & finding relationships.

Start at one end of the chain of pulleys or the other. Star at A or start at G.

If pulley A makes one complete rotation, how many rotations will pulley B make?

etc.

 

[DaveC426913]

You don't need a formula. You just need logic and patience.

A belt going from a smaller wheel to a larger wheel reduces the rotation rate.
A belt going from a larger wheel to a smaller wheel increases the rotation rate.

So G is actually going the <strike>slowest</strike> [ edited ] fastest of all.

[ Derp - Sammy beat me to it. ]

 

[jedishrfu]

So you start with A and notice that as A turns 1 revolution it will turn B say 1/2 rev.
Since B turns 1/2 then C turns 2 revs...

Then review the speeds of revolutions to get the answer.

 

[jedishrfu]

You don't need a formula. You just need logic and patience.

A belt going from a smaller wheel to a larger wheel reduces the rotation rate.
A belt going from a larger wheel to a smaller wheel increases the rotation rate.

So G is actually going the slowest of all.

[ Derp - Sammy beat me to it. ]

I think you meant to say B, right?

 

[jedishrfu]

@jedishrfu I think we were trying to get OP to do this.

Sorry, I just wanted to show the first step or two. I was actually composing my post before I saw yours.

 

[SammyS]

Sorry, I just wanted to show the first step or two.

OK.

I deleted my previous reply to you.

 

[Confused101]

The correct answer is B as you can see on the diagram. I get to start at A - Let's say it turns once, which caused B to turn half. If B is attached to the Blue B behind then that turns a quarter yes. which turns C red pulley half, and C Yellow pulley will turn once and if you go on like that G then turns only a 1/4 and I think should be the answer compared to B which only turns 1/2

 

[SammyS]

The correct answer is B as you can see on the diagram. I get to start at A - Let's say it turns once, which caused B to turn half. If B is attached to the Blue B behind then that turns a quarter yes. which turns C red pulley half, and C Yellow pulley will turn once and if you go on like that G then turns only a 1/4 and I think should be the answer compared to B which only turns 1/2

Both pulleys at B rotate together. Both rotate 1/2 turn, or both rotate 1/4 turn.

 

[Confused101]

Nope Just do not see it I am afraid. If A turns once and B turns 1/2 then surely C should turn once again - how do you make it 2 ?

 

[DaveC426913]

I think you meant to say B, right?

Perils of too much editing.
I actually meant G is fastest of all. I didn't want to give him the answer directly, just show him the logic and let him work it out.
I've fixed. it.

 

[DaveC426913]

Consider starting somewhere other than A. Both A and C are going to turn faster than B (since they're smaller) so you know they're not the answer.

 

[Confused101]

Guys. I have been staring at this for 4 hours so maybe you would like to talk me through the first 4 - 5 steps starting from A please

 

[DaveC426913]

Don't start at A. Start anywhere else.

Start at C.
B rotates slower than C.
D rotates the same as C.
E rotates faster than D.
etc.

 

[Confused101]

I work logically so starting at A seems a good a place as any. If A turns once, then B turns half. If B turns half, then C should turn once or is it twice ? and can you explain to me which is correct and how you worked it out, then I can go from there thanks .

 

[DaveC426913]

I work logically so starting at A seems a good a place as any.

How's that working out for you?

It not as good as anywhere else because it's the most complex and most confusing.

 

[Confused101]

Again how do you get from 1/2 B to 2 at C . I can only see it as 1 at C. It is half the size of the Blue wheel in B which has turned Half so thus its rotation is double that which is 1. The yellow C pulley which attached to the outer red should also then only turn once no ?

 

[scientific601]

From B to C is a factor of x2. So the current speed of 0.5 will increase to 1.

 

[Confused101]

Thanks for your help Scientific601. So A turns once, and B turns 0.5. C turns x 2 of B which is 1 turn. C turns once, so D turns once. If D turns once, then E turns x 4, so turns 4 times. If E turns 4 times, then F turns x 8. If F turns 8 then G turns 4 times. So B is the answer as it turns only 1/2 rotation. Is this correct. ?

 

[scientific601]

Barring any computational errors, yes. As the screenshot's answer agrees. The slowest in the train.