Vector Question on Ropes: Finding Forces with Angles | Homework Help

[J89]

Homework Statement

Problem:

Two ropes in a vertical plane exert equal magnitude forces on a hanging weight but pull with an angle of 86 degrees between them. What pull does each one exert if their resultant pull is 372 Newtons directly upward?

Homework Equations

Use sin and cos method??

The Attempt at a Solution

I did 372 sin 86 and 372 cos 86 and got 371 and 25...however I'm sure it's wrong because it does not add up to 372, but does equal to the magnitude of 86 degrees. Don't know what I am missing..help!

 

[LowlyPion]

Welcome to PF.

Think of it as a vector addition problem.

The vector magnitudes are equal. And the resultant vector is straight up.

That means that for the horizontal components to cancel, (result is vertically only) they must be equal and opposite.

This also means that the vertical component of each must then be equal and in the same direction because their magnitudes are equal.

Moreover they must both be at the same magnitude angle - opposite direction with the vertical.

Now you have all you need to know. the angle with the vertical 86/2 and the vertical component that is the Cos43 of the tension and that equals 372/2.

 

[J89]

Welcome to PF.

Think of it as a vector addition problem.

The vector magnitudes are equal. And the resultant vector is straight up.

That means that for the horizontal components to cancel, (result is vertically only) they must be equal and opposite.

This also means that the vertical component of each must then be equal and in the same direction because their magnitudes are equal.

Moreover they must both be at the same magnitude angle - opposite direction with the vertical.

Now you have all you need to know. the angle with the vertical 86/2 and the vertical component that is the Cos43 of the tension and that equals 372/2.

Ok, I sort of understood where you are coming from, but not completely. So the force would be 186/cos43= 254.3 Newtons total right?

 

[LowlyPion]

Ok, I sort of understood where you are coming from, but not completely. So the force would be 186/cos43= 254.3 Newtons total right?

Draw a diagram and draw the two cords holding the object.

The angle that you know is the angle it makes with the vertical because since the tensions are equal the vertical will be splitting the 86° angle between the cords.

The vertical component is what must account for the portion of the weight it is carrying. That would be 1/2*372 since the tensions are equal between the two.

Since that is the adjacent side to the angle, that means that Cos43°*T = 186. And you get the result that you indicated.