How Do You Calculate the Correct Components of a Force Along Tether Lines?

[quantum_enhan]

Homework Statement

A resultant vertical force of 1750 N is necessary to held the balloon in place. Resolve this force into components along the tether lines AB and AC, and compute the magnitde of each force.

The angle between AB and the vertical force is 40 deg, and the angle between AC and the vertical force is 30.

The Attempt at a Solution

After applying parallelogram law, I was able to produce a triangle with the angles 110, 40, and 30. I applied sine law as follow:

Fab / sin30 = 1750 / sin 110 = Fac / sin40

However, after computing, the answers are WAY off. I'm talking ~800-900 Newtons.

The answers in the back of the book are Fab = 186N and Fac = 239 N.


I just don't see how those components and angles given in the question can remotely come near the 1750 N force.. Help?>

 

[pongo38]

I suggest you draw the parallellogram to scale, and develop two equations representing vertical components and horizontal components. Check your answer by measurement of the scale drawing.

 

[quantum_enhan]

I have done so, but again I am getting entirely different answers. Perhaps someone can point me in the right director for vector allignment? I am assuming that its my arrangment of vectors that is corrupting my answer.

 

[pongo38]

"The answers in the back of the book are Fab = 186N and Fac = 239 N. "

Diagram looks ok. Book answers don't.

 

[rwisz]

As a scientist, it is important to check our calculations and make sure we are using the correct equations and values. In this case, it seems that the angles given in the question may not be correct or may have been misinterpreted. It is also possible that there are other forces acting on the balloon that are not mentioned in the question.

To resolve the force vector accurately, we need to have a clear understanding of the angles and directions involved. I would recommend double-checking the given angles and using a vector diagram to accurately determine the components along the tether lines. Additionally, it may be helpful to consider any other forces acting on the balloon, such as wind or air resistance, to get a more accurate result.

In science, it is important to always question and verify our results to ensure accuracy. I would suggest reviewing the problem and seeking clarification if needed to arrive at the correct solution.