Caternary Problem: Solve for Tension & Angles

[Radarithm]

Homework Statement

In most problems in this book, the ropes, cords, or cables have so little mass compared to other objects in the problem that you can safely ignore their mass. But if the rope is the only object in the problem, then clearly you cannot ignore its mass. For example, suppose we have a clothesline attached to two poles (Fig 5.61). The clothesline has a mass $M$ and each end makes an angle $\theta$ with the horizontal. What are (a) the tension at the ends of the clothesline and (b) the tension at the lowest point? (c) Why can't we have $\theta=0$? (d) blahblahblah [For a more advanced treatment of this curve, see K.R. Symon, Mechanics, 3rd Ed)

Homework Equations

Newton's Laws

The Attempt at a Solution

Unfortunately, I have absolutely no experience with problems such as this. My work is here (look at the second attempt, the first one was garbage): http://s15.postimg.org/xoou3zhh7/IMG_0743.jpg , and I am pretty sure I have the wrong answer; if I feel like it's too easy I'm definitely doing it wrong.

 

[Saitama]

Homework Statement

In most problems in this book, the ropes, cords, or cables have so little mass compared to other objects in the problem that you can safely ignore their mass. But if the rope is the only object in the problem, then clearly you cannot ignore its mass. For example, suppose we have a clothesline attached to two poles (Fig 5.61). The clothesline has a mass $M$ and each end makes an angle $\theta$ with the horizontal. What are (a) the tension at the ends of the clothesline and (b) the tension at the lowest point? (c) Why can't we have $\theta=0$? (d) blahblahblah [For a more advanced treatment of this curve, see K.R. Symon, Mechanics, 3rd Ed)

Homework Equations

Newton's Laws

The Attempt at a Solution

Unfortunately, I have absolutely no experience with problems such as this. My work is here (look at the second attempt, the first one was garbage): http://s15.postimg.org/xoou3zhh7/IMG_0743.jpg , and I am pretty sure I have the wrong answer; if I feel like it's too easy I'm definitely doing it wrong.

Hi Radarithm!

The tension acts along the rope, not horizontally. You only need to show mg at the centre of rope. Can you proceed now?

 

[Radarithm]

Doesn't the tension (on one end) need to support only half of the rope?

 

[Saitama]

Doesn't the tension (on one end) need to support only half of the rope?

Nope but its component would do. ;)

 

[Radarithm]

Got the answer I was looking for. Thanks for the help!

 

[tiny-tim]

nice

btw, it's catenary ​

(from the latin "catena" meaning "chain", cf. concatenation)

 

[Radarithm]

nice

btw, it's catenary ​

(from the latin "catena" meaning "chain", cf. concatenation)

*facepalm* Thanks for correcting me.