A rope of 5m is fastened to two hooks 4m apart on a horizontal ceiling

[verb tense]

Homework Statement

A rope of 5m is fastened to two hooks 4m apart on a horizontal ceiling. To the rope is attached 10kg mass so that the segment of the rope are 3m and 2m.Compute the tension in the string

Homework Equations

Sine rule

The Attempt at a Solution

I get stuck at the part that says '10kg mass so that the segment of the rope are 3m and 2m'. Please i just need the right diagram i know what to do.

 

[grzz]

Let us imagine we are hanging the mass to the rope.Right?

 

[verb tense]

Yes.

 

[grzz]

So if one fastened a 5m rope to two hooks at a horizontal distance 4m apart, the rope will hang in a curve. But when the mass is hung at the specified point, what will happen to the rope? (assume the rope does not extend)

 

[grzz]

We are trying to do it together!

 

[verb tense]

A triangle is formed.

 

[grzz]

So one knows the all the sides of this triangle. But I do not think that he sine rule can be used because there are to many unknowns for this rule to be used. Hence one can use the cosine rule to find the angles.

 

[verb tense]

Ok let me try it out.

 

[verb tense]

I got the angles to be 104,47 and 29 am i right and what next?

 

[grzz]

Correct but it is better to work with 104.5, 46.6 and 29.0 deg.

Now you can either use the sine rule or use components of the tensions.

 

[grzz]

Here is a diagram.

 

[verb tense]

i got the tension to be 73.5N and 49.1N

 

[grzz]

if you show the working I can tell you where there is something not correct.

 

[verb tense]

Here it is.

 

[grzz]

Using the sine rule is ok but it is being used in the wrong triangle. Note that the tiangle of the set up of the apparatus is not necessarily a traingle of forces. In fact the triangle you are using is a traingle of distances not forces.

Try to draw a triagle of the forces showing the directions of the weight, tension1 and tension2. Then put the angles required for this traingle of forces. If you need further help just ask.

 

[verb tense]

Need help don't know what to do.

 

[grzz]

Look at the diagram of the forces and fit in its angles using information form the diagram of the apparatus.

 

[verb tense]

Ok is this it?

 

[grzz]

How can the angle at the bottom of your diagram be 104deg if it must be LESS than 90deg.
Try again to get the angles of the FORCES diagram. The information required for this can be obained from the diagram of the strings attached to the mass.

 

[grzz]

For example tension T1 will make angle 43.4deg with the vertical.

 

[verb tense]

I think i got it

 

[grzz]

That is correct!

Remember. There is a diagram for the distances and a diagram for the forces.

 

[verb tense]

Okay , so this is what i got for tension 88.5N and 69.5N

 

[grzz]

Correct.

There is another way how to do it.

 

[verb tense]

Ok, Thanks.

Please can you show me the other way to do it?

 

[grzz]

One starts from the diagram in the attachment. Then the vertical and horizontal components of the tensions are drawn.Try to do that.

 

[grzz]

... and then one can compare the two methods.