Confirmation of a net force calculation from a diagram

[Humbleness]

Homework Statement

Calculate the net force acting on the object indicated in the following diagram. Show your work.

Homework Equations

cosine/sine law

The Attempt at a Solution

First I subtracted 10N and 8N (since they are forces acting in different directions):
-8.0N (S) + 10.0N (S) = 2.0 (S)

Then I used the tip-to-tail method:

First using cosine law to find magnitude of the net force:
c² = a² + b² - 2abcosC
c² = 4 + 289 - 2 x 2 x 17 (cos45)
c² = 293 - 48
c = 15.6N

Now angle using sine law:
sina/2.0N = sinb/17N = sin45/15.6N
b = sin^-1 (sin45/15.6 x 17)
b = 50.4

Therefore, the net force is 15.6N (S 50.4 W) West of South

 

[lewando]

Your resultant magnitude looks right, but your angle (as reported: "S 50.4 W") does not. The angles are close, so if you want to go with "S <angle> W" notation, then then your B vector would have an angle of "S 135 W". Think about it.

 

[Humbleness]

The angles are close, so if you want to go with "S <angle> W" notation, then then your B vector would have an angle of "S 135 W". Think about it.

I think I understand what I did wrong regarding the angle. As far as I can tell based on the original diagram, 17N is (N 45 W), therefore, the angle of the net force should be (N 50.4 W). Does this look right?

 

[lewando]

Looks much better, except I got a slightly different value because I held on to an extra digit in the magnitude result (15.65), when doing the sin rule calculation.

 

[CWatters]

I haven't had time to check your working but your diagram looked wrong to me. You appear to be doing tail to tail rather than head to tail if you see what I mean.

I'm on my phone at the moment but will try and post again later.

 

[Humbleness]

Looks much better, except I got a slightly different value because I held on to an extra digit in the magnitude result (15.65), when doing the sin rule calculation.

After re-doing the calculations, I got the same result (15.65).
So it would actually end up being: 15.65N (N 50.2 W).
Is this what you got?

 

[lewando]

Yes. 15.65 is over-precise, given the digit-significance of the values in the problem statement. It is good to be overprecise during intermediate calculations.

 

[Humbleness]

I haven't had time to check your working but your diagram looked wrong to me. You appear to be doing tail to tail rather than head to tail if you see what I mean.

I'm pretty sure I used head-to-tail in my diagram, I don't think I got that part wrong.

 

[CWatters]

I haven't had time to check your working but your diagram looked wrong to me. You appear to be doing tail to tail rather than head to tail if you see what I mean.

I'm on my phone at the moment but will try and post again later.

Ignore this. Your diagram is correct, I miss-read it.

 

[Humbleness]

Okay, thank you though as well for checking out, I always like to receive confirmations of whether my work is correct, since I am doing this course online, and it's difficult with no teacher present or class peers with whom I can verify my work, hence why it is good that forums such as these exist.