# Find mass of rope

1. Apr 28, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
One end of a rope is fixed to a vertical wall and the other end pulled by a horizontal force of 20N. The shape of the flexible rope is shown in the figure. Find its mass.

2. Relevant equations

http://www.luiseduardo.com.br/mechanics/static/staticproblems_arquivos/image017.jpg [Broken]

3. The attempt at a solution

Let the wall exert a force F in the tangential direction at the point where rope is fixed. Let the tangent make an angle θ with vertical.
Fcosθ=mg
Fsinθ=20

cotθ= mg/20

But θ is still unknown!

Last edited by a moderator: May 6, 2017
2. Apr 28, 2014

### projjal

Without θ question is incomplete. The horizontal force applied is 20N : only this information cannot determine the mass of the rope.

3. Apr 28, 2014

### SteamKing

Staff Emeritus
Not so fast! The OP hasn't even begun to analyze the rope.

This is a well-known problem in physics, analyzing suspended ropes and chains. There is a solution, and the answer might surprise you.

http://en.wikipedia.org/wiki/Catenary

4. Apr 28, 2014

### projjal

Well, sorry for my incomprehensibility.Its first time I came across such problem.

Last edited: Apr 28, 2014
5. Apr 28, 2014

### utkarshakash

Hmm, the article is difficult to understand. Can you please guide me step-by-step on how to solve this problem? I think finding the equation for the curve should be my first step. But I don't have any idea how to do that.

6. Apr 28, 2014

### SteamKing

Staff Emeritus
You don't have enough information to do all the detailed calculations. However, take a look at the results obtained in the 'Analysis' section of the Wiki article. There's your answer (with a helpful diagram showing all the forces acting on the rope.

7. Apr 28, 2014

### PhanthomJay

The figure or statement seems to be missing information. I can take a piece of thin rope and pull on it horizontally with a force of 20 N, and then I can take a piece of heavier rope and pull on it horizonatlly with the same force. In the latter case, the sag will be greater and the angle sharper, but with that info missing, I cannot calculate the mass or weight of the thread.