Magnitude and Component Question

1. Jan 20, 2010

jegues

1. The problem statement, all variables and given/known data
Determine the magnitude of the u and v-components of the 4kN force shown in the figure.

2. Relevant equations

3. The attempt at a solution

I'm confused, am I suppose to assign u and v a magnitude and direction in order to obtain a resultant force of 4kN horizontally?

The answers in the book are given as follows:

u = 4.11 kN
v = 2.44 kN

If I'm suppose to answer the question the way I think I do then,
$$Fy=Usin(35) + Vsin(105) = 0$$

Also,

$$Fx=Ucos(35) + Vcos(105) = 4$$

2 equations, 2 unknowns I can solve it but I don't think I'm doing this the right way, any ideas?

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2. Jan 20, 2010

vela

Staff Emeritus
No, they're asking you to find the projection of F onto U and onto V. The projections won't add to equal F.

3. Jan 20, 2010

jegues

How do I go about finding the projection of F onto U and onto V? Also, I don't really know what you mean by projections so that might be what's stopping me from solving this problem.

4. Jan 20, 2010

vela

Staff Emeritus
Sorry, I was wrong. I was thinking of a different problem. The two components will sum to F.

Did you finish solving for U and V the way you started? It looks okay to me.

5. Jan 20, 2010

jegues

So is my original "attempt" at the solution in my OP correct?

Also, it doesn't give the sense of the forces, only the line of action. It seems to me that this could have numerous possible solutions.

6. Jan 20, 2010

vela

Staff Emeritus
I think your approach will work. The answer will be unique because the vectors along the U and V direction are linearly independent.

7. Jan 20, 2010

jegues

For V I get,

V = 10.12 and U,

U = 17.05

What do you think?

Also, are the answers in the book wrong?

8. Jan 20, 2010

vela

Staff Emeritus
Those answers seem way off. I got different answers, but they don't match what your book got.

9. Jan 20, 2010

jegues

What'd you do?

I'm still not even sure if we're taking the right route to solving this question, or if we're even solving for the desired quantity.

I'm curious as to your approach.

10. Jan 20, 2010

vela

Staff Emeritus
I solved your equations. :) I think you just made an algebra mistake when solving for U and V.

11. Jan 20, 2010

jegues

Hmmm the second time solving I got V = 20.78 and U = 35.

This any better?

12. Jan 20, 2010

jegues

My method for solving the problem doesn't seem to make any sense since both the Fy components would be positive and I need them to cancel out.

13. Jan 20, 2010

vela

Staff Emeritus
No. Worse actually. You can check your answer by plugging it back into your equations and seeing if the sums work out correctly.

How are you solving the equations? I find Cramer's rule to be a good way to solve them.

14. Jan 20, 2010

jegues

I managed to solve it.

The answers the book indicated are correct, thanks for the help!

15. Jan 20, 2010

vela

Staff Emeritus
Great! It turns out I was in radians mode, which is why I wasn't getting the correct answers.