# Force equations: Force on ground by angled supports

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1. Sep 28, 2016

### rihitz

1. The problem statement, all variables and given/known data

P=60kN
angle alpha = 45 degrees
angle beta = 20 degrees

The task is to calculate the force on the base A and C, and to draw vectors that represent those forces.

2. Relevant equations

3. The attempt at a solution
I did similar examples at the class, but when I had to do this one on the test, I just could not get it done.

If I could get the balanced equations down correctly, I would manage to do the rest. (balanced force equations on x and y axis)

Sorry if there are wrong terms used, Im not a native speaker. Ill try to explain if there is anything unclear.

Thanks!

2. Sep 28, 2016

### RUber

What have you tried so far?

I'm no physicist, but I would think that some there might exist some r, such that r*(sin 20 + sin 45 ) = 60. This might help you balance out the y direction.

3. Sep 28, 2016

### rihitz

Well the R should be right above the P in that case, which cancels the P itself. But that didnt help me out. Or im drawing something incorectly

4. Sep 28, 2016

### RUber

I was thinking that r would be a scalar...rsin(20) is the y component of the vector acting at point C, r sin 45 would be the y component of the vector acting at point A.

5. Sep 28, 2016

### RUber

Or perhaps that is too simple. Let's take another look at this...
You have two force vectors W and V, each one has magnitude |W| and |V|, respectively.
You want to find those magnitudes such that the following equations are satisfied:
$|W| \sin 45 + |V| \sin 20 = 60$
$|W| \cos 45 = |V| \cos 20$
Does that seem more reasonable?

6. Sep 28, 2016

### rihitz

I am a bit confused.

Is this equation for the projection of all forces on y axis wrong?

7. Sep 28, 2016

### rihitz

I also dont get why on the second equation both magnitudes have to be equal? Id say they wont be equal, since the angles are different

8. Sep 28, 2016

### Staff: Mentor

If F and G are the compression forces in rods AB and BC, what are the components of these forces in the x- and y directions?

9. Sep 28, 2016

### rihitz

In the picture F and G is Fw and Fv. Is that right? In that case components are. P/sin45 and P/sin20 for the y axis. And P*cos45 and P*cos20 for the x axis. Atleast if I got it right.

10. Sep 28, 2016

### Staff: Mentor

You didn't get it right.

Step 1 - Forget about P.

Step 2 - From the trigonometry, what are the components of F and G in terms of F, G, and the angles.

11. Sep 28, 2016

### rihitz

Like this?

12. Sep 28, 2016

### Staff: Mentor

Yes. Very nice.

The signs on the G components should be - in the x direction and + in the y direction. Now, using the upper junction point as your free body, do a force balance in the x direction and a force balance in the y direction on the junction point. What do you get?

13. Sep 28, 2016

### rihitz

I hope I understood correctly what you asked due to the language barier.

But I guess this is what you meant:

14. Sep 28, 2016

### Staff: Mentor

Excellent. Now solve for F and G.

Also, now compare with Ruber's post #5.

15. Sep 28, 2016

### rihitz

Is this correct?

16. Sep 28, 2016

### Staff: Mentor

Your methodology is correct. I didn't check your algebra. If you want to do that, just substitute your results into the two force balance equations and see if the equations are satisfied.

17. Sep 28, 2016

### rihitz

Great! Thanks! To both of you.
So my mistake was that I tried to make components of F and G from P? While I actually had to make them from the F and G itself.

18. Sep 29, 2016

### rihitz

Im sorry. Could you please tell me where Im wrong again? I am using the same methodology, but I have a feeling its incorrect, cause I cant find the second force momentum equation.

The A, Ax, Ay, C , Cy and Cx is added by me. Everything else was given.

19. Sep 29, 2016

### rihitz

Why am I getting a negative Cy, when it should be positive?

20. Sep 29, 2016

### haruspex

I do not understand the connection between this post and the rest of this thread. What are Ax etc.?