Solving Physics Problem - Wrong Answer for F2

[Ryuk1990]

This is a physics problem where I need to solve for F1 and F2. What am I doing wrong because I am not getting the right answer for F2. It's not even supposed to be negative.

 

[Redbelly98]

There are two problems here.

1. In the last step, you incorrectly evaluated the denominator,

-sin(26.6) + cos(26.6)*cos(21.8)/sin(21.8)​

It does not equal 2, as you seem to have calculated.

2. The correct answer for F2, given the 2 equations you are starting with, is negative. If that is wrong, there is a problem in how you derived those two equations.

 

[Ryuk1990]

Ok, here's how the force components are set up. Are the equations right for it?

 

[Redbelly98]

Looks like the equations are set up correctly, at least on the left-hand sides. So I have two followup questions for you:

1. Why must the forces sum to zero?

2. Why can't F2 be negative? That would simply mean it points in the upward-rightward direction, instead of downward-leftward as drawn.

By the way, in the future, it would be helpful if you post the actual full problem statement

 

[Ryuk1990]

Looks like the equations are set up correctly, at least on the left-hand sides. So I have two followup questions for you:

1. Why must the forces sum to zero?

I don't know the theory behind why but that's how I was taught to solve these kind of problems where I need to find the magnitudes of the force components.

2. Why can't F2 be negative? That would simply mean it points in the upward-rightward direction, instead of downward-leftward as drawn.

I see what you mean. It's just that the book didn't give the answer as negative so I got confused. All it said was 1180 N (that's rounded) with no negative sign or direction given.

 

[Redbelly98]

Well, it depends what the question is, but I have absolutely no idea what was being asked.

Have you recalculated F2 based on what I said in Post #2?

 

[Ryuk1990]

Well, it depends what the question is, but I have absolutely no idea what was being asked.

Have you recalculated F2 based on what I said in Post #2?

Yeah, I did recalculate and I got -1176.

Here's how the question reads:

Two forces F1 and F2 are applied as shown in Fig. 7.31(which is the diagram I posted above). The resultant R has a magnitude of 850 N and acts in the direction shown in the figure. Determine the magnitudes of F1 and F2.

That's all it says.

 

[Redbelly98]

You have magnitude that agrees with the final answer now, so that is progress. But, you set up the equation wrong earlier. The resultant is, by definition, the sum of the other vectors F₁ and F₂.

Instead of

F_1x + F_2x + R_x = 0​

it should be

F_1x + F_2x = R_x​

and similarly for the y-components.