# Find the speed of a knot on rope

1. Oct 28, 2012

### VHAHAHA

1. The problem statement, all variables and given/known data

http://s12.postimage.org/q2c8bqw97/image.png

http://i.imgur.com/6STfr.png

The part a is easy and i get the ans, the required speed should be v/cos30
but i really have no clue about how to do the part b
i know that the knot will move down and left but i just can't list any equation for the motion

2. Relevant equations
the length of string is constant

3. The attempt at a solution
i use √X^2 + Y^2 = constant is part a
and get the v/cos 30

but i really have no idea about b part

#### Attached Files:

• ###### question.zip
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25.9 KB
Views:
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Last edited: Oct 28, 2012
2. Oct 28, 2012

### PeterO

Not sure if you have noticed, but the image has not come through? Not here anyway.

3. Oct 28, 2012

### VHAHAHA

you can't see the image???

4. Oct 28, 2012

### PeterO

Until I hit quote, I didn't even realise you had tried to include one. The imbedded image code showed up among your text.

EDIT: the image reference just appeared in the original post.

EDIT 2: But the image is too small to read, and has insufficient resolution to be enlarged ??

5. Oct 28, 2012

### VHAHAHA

i have now giving the website of image

can u see now?

I am now updating the zip file

is it ok???

Last edited: Oct 28, 2012
6. Oct 28, 2012

### VHAHAHA

hope it is all right

7. Oct 28, 2012

### PeterO

Image works, but it is 2:00 am here and I am about to go to bed.

8. Oct 28, 2012

### VHAHAHA

thank you and have a good dream =D

9. Oct 28, 2012

### PeterO

OK,

I see that the pulley is supposed to be infinitely small, so is to be represented as a point on the bottom rail matching the other geometry restraints.

Can you calculate how far K is from B [or from the pulley for that matter, since it is in the middle of the rope] at the "30o" situation.
btw: you should be able to calculate that distance without reference to a pen, paper or calculator. [hint: 2,1,√3 ]

You can get a guide to the answer by establishing where K was when the angle was 29o and 31o and calculating the time taken for that change.

10. Oct 28, 2012

### PeterO

Just to let you know how I am visualising the situation.

Clearly as the string is drawn in, the knot, K, gets closer to the pulley, O, and at the same time the angle, θ, is going to get larger, until it reached 90o.

Lets imagine those changes separately.
Considering only the angle change - I see K tracing out a circular arc, going up and left. [I can draw that in my mind or sketch it on paper]
I then imagine a series of radii drawn to that arc.
Considering that K is actually getting closer to O, I then see that K would actually be spiraling down towards O.

I am then faced with the calculus to describe that situation!!

11. Oct 28, 2012

### VHAHAHA

yes. i share the same idea with u. i think we can use polar coor. i am on my way back home and i will upload my calculation. thank you

12. Oct 29, 2012

### VHAHAHA

I have figure out the solution ( maybe)

I use polar coor. to find the speed

the only problem is that i have to find the angular velocity

let the angle be θ and let the radius of the Sector be L

i found that if i consider the arc length and use
Ldθ = dx that would give a wrong ans

if i consider the area
so that (1/2) L^2 dθ = (1/2) dx H where H is the height

i will get the right ans

the attached file is my steps

plz help me and thank you for your clue, It proved that my original idea is right , i just lack of confidence =D

#### Attached Files:

• ###### NewDoc.pdf
File size:
985 KB
Views:
63
13. Oct 29, 2012

### PeterO

have you noticed that the geometry of the 30o position gives a very special relationship between the distances OK or BK (they are equal of course since K is the midpoint) and H

14. Oct 29, 2012

### VHAHAHA

similar trian?

i am not good at geometry =(

do i get the right ans in my pdf? thank you

also, the horizontal distance between k and b is √3 /2 h

the vertial is h/2 ???

the angle 30 gives sin 30 =1/2 cos 30 = √3 /2 <-- this special relation ?

Last edited: Oct 29, 2012
15. Oct 29, 2012

### PeterO

I believe at this position, the distance you are calling L is equal to H, so there is one less variable than you have.
I can't follow your calculation: looks to me to be more of an advanced maths problem than Introductory Physics one.

16. Oct 29, 2012

### VHAHAHA

so i need to post to the advanced mechanics ?
i am moving now plz del this post

and thank you for your help! =D

Last edited: Oct 29, 2012
17. Oct 29, 2012

### VHAHAHA

1. The problem statement, all variables and given/known data[/b]

http://s12.postimage.org/q2c8bqw97/image.png

http://i.imgur.com/6STfr.png

this post is moved from the introductory physics as this actually involves advanced mechanics

The part a is easy and i get the ans, the required speed should be v/cos30

but the part b is the thing that i can't understand

i actually use polor coor. to get b ans and it seems right as when i assume the speed v be a certain number, and the find the speed after 0.000001 , the ans is equal that ans calculated from from my equation

2. Relevant equations
the length of string is constant
the area of the triangle

3. The attempt at a solution
i use √X^2 + Y^2 = constant is part a
and get the v/cos 30

in part b

it's difficult to explain and i just upload my steps

the problem is that if i use s=rθ the equation will be wrong

but if i use the area of sector = 1/2 l^2 θ = 1/2 b x h where b is the base and h is the height and l is the radius

i will get correct ans

can anyone help ?

the attached pdf is my steps
http://pdfcast.org/pdf/dsada-dsad-as-das [Broken] <-- this is the steps that plugging the valve v and assure my equation is correct

Last edited by a moderator: May 6, 2017
18. Oct 29, 2012

### VHAHAHA

can anyone provide a ans to me? my answer is right or wrong?

19. Oct 29, 2012

### haruspex

You have the speed and direction of the string at B. Think about the speed and direction of a point on the string OB near to O. Point K is halfway between the two. What do you think the relation would be between the three velocities?

20. Oct 29, 2012

### VHAHAHA

the speed of a pt near O is pointing downward??? with speed v ???