What is the Resultant Force from adding these two forces?

[DIANAWIELT]

Homework Statement

the resultant of two forces F1 AND F2 equel R , the second force F2 reversed its direction and the resultant become square root of 3 *R find the angle between these two force?

Relevant Equations

the resultant of two forces F1 AND F2 equal R , the second force F2 reversed its direction and the resultant become square root of 3 *R find the angle between these two forces?

when is apply the formulae of resultant force for the two equations the angles cancel out and I can't get any value for the angle when i add the two equations:
R^=f1^2+f2^2+2f1f2cos(theta)
squart3*R=f1^2+f2^2-2f1f2cos(theta)

 

[haruspex]

Homework Statement: the resultant of two forces F1 AND F2 equel R , the second force F2 reversed its direction and the resultant become square root of 3 *R find the angle between these two force?
Relevant Equations: the resultant of two forces F1 AND F2 equal R , the second force F2 reversed its direction and the resultant become square root of 3 *R find the angle between these two forces?

when is apply the formulae of resultant force for the two equations the angles cancel out and I can't get any value for the angle when i add the two equations:
R^=f1^2+f2^2+2f1f2cos(theta)
squart3*R=f1^2+f2^2-2f1f2cos(theta)

I assume your first equation is intended as $R^2=f_1^2+f_2^2+2f_1f_2\cos(\theta)$.
You forgot to square the LHS in your second equation. Or maybe you thought it meant the resultant becomes $\sqrt{3R}$. To be dimensionally consistent it must mean $\sqrt 3R$.

 

[nasu]

Are the two forces equal in magnitude? What is the complete statement of the problem?

 

[haruspex]

Are the two forces equal in magnitude?

It is not necessary to assume that.

 

[nasu]

Then the answer depends on the ratio of the two forces. For some ratio there is no answer. For example, if one force is f and the other 0.1f, the resultant will be between 1.1f and 0.9 f for all possible angles. There is no way to have an angle where the resultant is about 1.73 times the resultant for a different angle

 

[haruspex]

Then the answer depends on the ratio of the two forces. For some ratio there is no answer. For example, if one force is f and the other 0.1f, the resultant will be between 1.1f and 0.9 f for all possible angles. There is no way to have an angle where the resultant is about 1.73 times the resultant for a different angle

True, but the question states that these two forces are such that the resultants have the given relationship. That there are other force magnitudes for which such a relationship is not possible is of no concern.

 

[nasu]

I mean the ratio between the forces (F1 and F2), and not between the resultants, which is given.
For a given relationship between resultants, the angle at which this realtionship happens depends on the ratio between the magnitudes of the two forces. Just as an example: if the two forces are equal the angle is 120 degrees. If one of them is twice as large as the other, the angle is about 128.7 degrees and not the ame 128 degrees. There is an interval of the ratio between F1 and F2 for which the ration between the resultants is $\sqrt{3}$ at a specific angle which depends on this ratio.

 

[haruspex]

I mean the ratio between the forces (F1 and F2)

Yes, I understood that.

 

[nasu]

Then what do you mean by your previous comment? Do you mean that the angle does not depend on the relative size of the two forces?

 

[Lnewqban]

... when is apply the formulae of resultant force for the two equations the angles cancel out and I can't get any value for the angle when i add the two equations:
R^=f1^2+f2^2+2f1f2cos(theta)
squart3*R=f1^2+f2^2-2f1f2cos(theta)

Welcome, @DIANAWIELT !
This diagram shows that those angles are not cancelled out.

 

[haruspex]

Then what do you mean by your previous comment? Do you mean that the angle does not depend on the relative size of the two forces?

No, but the two forces are given, so they can appear in the answer.

 

[haruspex]

Welcome, @DIANAWIELT !
This diagram shows that those angles are not cancelled out.

View attachment 331432

@DIANAWIELT … but please note that @Lnewqban's diagram assumes the forces are equal in magnitude. It is not clear whether you are supposed to assume that (unless you missed that out in post #1).

 

[Steve4Physics]

@DIANAWIELT, if you are still reading this...

I can't get any value for the angle when i add the two equations

Then don't add the equations!

R^=f1^2+f2^2+2f1f2cos(theta)
squart3*R=f1^2+f2^2-2f1f2cos(theta)

There are mistakes. The equations should be:
$R^2=f_1^2+f_2^2+2f_1f_2 \cos(\theta)$ and
$3R^2=f_1^2+f_2^2-2f_1f_2 \cos(\theta)$
because the resultant squared in the 2nd equation is $(R\sqrt 3)^2 = 3R^2$.

If you can eliminate $R^2$ from the two equations you can express $\theta$ as a function of $f_1$ and $f_2$ which (as already suggested by @haruspex) is probably what is required.

 

[nasu]

No, but the two forces are given, so they can appear in the answer.

If F1 and F2 are considered given, why not R as well? If you considered that they are all "given" you can find the angle right away. No need for the extra part about changing the sign of one of the forces. There is no hint in the OP that the answer should be in terms of F1 and F2 but not of R.
We are gain trying to guess what the problem is rather than asking the OP to clarify and waiting for his input before giving all kind of possible answers.

 

[haruspex]

We are gain trying to guess what the problem is rather than asking the OP to clarify and waiting for his input before giving all kind of possible answers.

True, but it's not such an issue here. An answer can be obtained as a function of f1/f2. If it turns out they are given as equal, the final step is trivial.

 

[nasu]

But te answer can be obtained as a function of F1,F2 and R. In an even more trivial way. Why dimiss R but keep F1 and F2? this is exactly the issue here. You "force" the given (possibly incomplete) statement based on what you consider more interesting. Which I agree, it is (most interesting statement). Not necessarily helpful to the OP.

 

[vela]

Is the OP even on the right track? The way I'd read the problem statement as stated is $\vec F_1 + \vec F_2 = \vec R$ and $\vec F_1 + (-\vec F_2) = \sqrt 3 \vec R$.

 

[nasu]

I don't know about the OP. But the OP statement does not contain vector notation. So far I considered that the resultant changes its magnitude but not that it keeps the same direction. Do you think that it will be possible to satisfy the two relationships as you wrote them?

Edit. You may be right. This may make the ratio of the two forces irrelevant. Have you seen the original statement of the problem somewhere else?

 

[vela]

No, I haven't seen the original problem anywhere else, but I do know that many students don't realize $\vec V$ and $V$ aren't the same thing. Plus, it's strange and sloppy to refer to the magnitude of the resultant as just the resultant. So it's easy for me to believe the OP left out the vector notation in the problem statement.

 

[haruspex]

Is the OP even on the right track? The way I'd read the problem statement as stated is $\vec F_1 + \vec F_2 = \vec R$ and $\vec F_1 + (-\vec F_2) = \sqrt 3 \vec R$.

Doesn’t that make all the vectors parallel?

 

[vela]

Doesn’t that make all the vectors parallel?

Or anti-parallel.