Problem using Pulleys with Weight in Equilibrium

[Tygra]

Homework Statement

Calculate angle of mast and the compression force in the mast

Relevant Equations

In the question

Dear all,

I have the following problem:

I need to find the compression "C" in the mast and the angle that the masts makes with the horizontal (X degrees).

I know that the tension in the ropes "T" are of the same magnitude on both sides of the pulley, but I am struggling with finding C and X.

Could someone help please?

 

[Lnewqban]

If nothing is moving, all forces are in balance.
What have you done so far in terms of free body diagrams?

 

[Tygra]

Hi Lnewqban,

this is how I attempt the question:

When I do the final algebra, I am way off.

 

[erobz]

Hi Lnewqban,

this is how I attempt the question:

View attachment 352905
When I do the final algebra, I am way off.

Please share a Free body diagram of the hanging weight, and a separate FBD of the mast.

 

[Lnewqban]

this is how I attempt the question:

It seems that the original diagram shows the top 45° angle in error, as its reference should be a vertical line rather than C.

For a good example of FBD related to this problem, look for the example in "Particle Equilibrium" here:
https://courses.lumenlearning.com/s...apter/6-1-solving-problems-with-newtons-laws/

 

[Tygra]

It seems that the original diagram shows the top 45° angle in error, as its reference should be a vertical line rather than C.

So are you saying they did this on purpose?

Can I ask, how you would attempt this question?

 

[Lnewqban]

No, I don’t.
Yes, you can: a free body diagram would be my very first step.

 

[Tygra]

No, I don’t.
Yes, you can: a free body diagram would be my very first step.

So it must be a typo in the book? This problem is from a book.

Here is my free body diagram:

Is this correct?

 

[erobz]

So it must be a typo in the book? This problem is from a book.

Here is my free body diagram:

View attachment 352917

Is this correct?

FBD of what? You isolate the hanging mass. Forces of weight $W$ and tension(s) $T$ act on it. You use it to find $T$ in terms of $W$. Thats one FBD. The other is a Free body diagram of the member $C$. You isolate the mast from the external surroundings. Tension forces, and reaction forces at the hinge should be shown. You use both component equations simultaneously to find the angle $X$.

 

[Tygra]

Thank you. I have it now. I think I was making it more complicated than what it was.

 

[Lnewqban]

So it must be a typo in the book? This problem is from a book.

Here is my free body diagram:

View attachment 352917

Is this correct?

Yes, it must be a typo.
Otherwise they would be giving away angle x as being 90° (45+45+90=180), which is an incorrect value.

In order to properly calculate T, you need to consider the “Y” formed by T, T and 5 kN.
In this case the “Y” is symmetrical and the value of T is the same on the left and the right sides, but it is not always that way.
Hope you have checked the example in the link previously posted.

 

[Lnewqban]

Thank you. I have it now. I think I was making it more complicated than what it was.

Please see:
https://roperescuetraining.com/physics_angles.php