Finding magnitude of two forces with given degrees ?

[kari7921]

Homework Statement

Two forces F1 and F2 are applied, F1 makes a 45 degree angle and F2 makes a 30 degree angle. The resultant R has a magnitude of 500 lbf and acts along the positive x-axis. Determine the magnitudes of F1 and F2.

Homework Equations

Pythagorean theorem?

The Attempt at a Solution

I thought using the pythagorean theorem would be used for this problem.
c^2=a^2 + b^2 - 2ab cos Csomebody pleaseeee help me :S

 

[Delphi51]

Welcome to PF, Kari.
Yes, not all that clear, is it? I think it means F1 is angled 45 degrees up from the x-axis and F2 is 30 degrees below the x-axis.
Sketch that! Let us label the magnitude of F1 as "a" and the magnitude of F2 as "b".

Two other facts are given.
1. the sum of the vectors is along the x-axis, so the sum of the y components is zero.
2. the sum of the x-components is 500.

Write an equation for each of those facts, based on your diagram, and you will be able to solve them as a system of 2 equations to find the magnitudes a and b.

 

[kerimek]

I would approach this problem by using vector addition and trigonometric functions. First, I would draw a diagram to visualize the given information and label the known angles and forces. Then, I would use the following equations to solve for the magnitudes of F1 and F2:

F1x + F2x = R

F1y + F2y = 0

where F1x and F1y are the x and y components of F1, F2x and F2y are the x and y components of F2, and R is the resultant vector with a magnitude of 500 lbf acting along the positive x-axis.

Using trigonometric functions, we can relate the angles and the components of the forces:

F1x = F1cos(45)

F1y = F1sin(45)

F2x = F2cos(30)

F2y = F2sin(30)

Substituting these equations into the first two equations, we get:

F1cos(45) + F2cos(30) = 500

F1sin(45) + F2sin(30) = 0

We can then solve for F1 and F2 by using algebraic manipulation and substitution. By solving for F1 and F2, we can determine their magnitudes. The Pythagorean theorem can also be used to check the solution, as the magnitude of the resultant vector R should be equal to the square root of the sum of the squares of F1 and F2:

R = √(F1^2 + F2^2)

I hope this helps. Let me know if you have any further questions.