Calculating Force and Angle Vectors | Help with Force/Vectors Homework

[vykim223]

Homework Statement

Given: >>http://postimage.org/image/vohuki2rr/<<
F1 = 250g, θ1 = 90°
F2 = 150g, θ2 = 210°
F3 = ?g, θ3 = ?°

a. Calculate the values for F3 and θ3.
b. Draw a diagram.

Homework Equations

R = A + B
R = A + B + C
F = √(Fx)^2 + (Fy)^2
θ = TAN-1(Fy/Fx)

The Attempt at a Solution

I've used to first and the third formula to solve for F3 and the last formula to try to solve for θ3 but my teacher told me that my answers were wrong. I'm just at a complete loss now on this problem. I've put up a link on top with the image that's part of the problem also. Could someone help me in the right direction? I don't want the answers but rather the proper way to go about solving this problem?

 

[BruceW]

Welcome to physicsforums, vykim223 :)

Your diagram is a bit odd. Why have you drawn it so that θ1 is much less than 90°? But anyway, the diagram doesn't really matter, since you are using the maths to solve this problem.

I'm guessing the problem is to solve so that the three forces add up to zero? Your relevant equations might be correct. It just depends on how you use them. Allright, so are you familiar with the idea of a vector? If we're saying the three forces sum to zero, then what does that mean mathematically? And considering that we are given two of the forces, what does that tell us about the last force?

 

[vykim223]

Welcome to physicsforums, vykim223 :)

Your diagram is a bit odd. Why have you drawn it so that θ1 is much less than 90°? But anyway, the diagram doesn't really matter, since you are using the maths to solve this problem.

I'm guessing the problem is to solve so that the three forces add up to zero? Your relevant equations might be correct. It just depends on how you use them. Allright, so are you familiar with the idea of a vector? If we're saying the three forces sum to zero, then what does that mean mathematically? And considering that we are given two of the forces, what does that tell us about the last force?

The diagram wasn't meant to scale to begin with cause I have 4 similar problems that goes with it. If I can solve this one problem then I'll be able to do the other 4 problems.
So if all three forces are supposed to add up to zero. Then the way to solve it is...
250g + 150g + F3 = 0
F3 = 400g?

θ = TAN-1(210°/90°)
θ = 66.80°?

I don't feel too confident in my answers. I could be very very wrong. I understand that in vectors the F3 must be equal in magnitude but opposite in direction to the R (F1+F2).

 

[emailanmol]

If the net force on a body is 0, then the component of forces along two perpendicular axis is 0. (Why?)(Hint:Vectors).

Write equations for vector components of force.Remember, force is a vector quantity.It follows vector addition laws.
Use these to obtain the answer.

 

[BruceW]

emailanmol has said some useful stuff. As he's implied, this question is really just testing your understanding of vectors.

So if all three forces are supposed to add up to zero. Then the way to solve it is...
250g + 150g + F3 = 0
F3 = 400g?

I'm guessing you meant F3 = -400g? But anyway, this is not right. It would be right if the forces were in 1d, but for this problem, we've got 2d, so you need to also consider the direction which each of the forces are pointing.

I understand that in vectors the F3 must be equal in magnitude but opposite in direction to the R (F1+F2).

Yes, that's right. So now you just need to find the direction and magnitude of F1+F2. You might find it easiest to do this by drawing out the problem, and using geometry. (That's what I usually do when I get a vector problem).