Question

As shown in the diagram, two forces act on an object. The forces have magnitudes F1 = 5.7 N and F2 = 1.9 N. What third force will cause the object to be in equilibrium?
3.8 N at 108° counterclockwise from

6.3 N at 162° counterclockwise from

3.8 N at 162° counterclockwise from

6.3 N at 108° counterclockwise from

Answer 1

Answer:

Second option 6.3 N at 162° counterclockwise from  F1

Explanation:

Observe the attached image. We must calculate the sum of all the forces in the direction x and in the direction y and equal the sum of the forces to 0.  

For the address x we have:  

$-F_3sin(b) + F_1 = 0$

For the address and we have:  

$-F_3cos(b) + F_2 = 0$

The forces $F_1$ and $F_2$ are known  

$F_1 = 5.7\ N\\\\F_2 = 1.9\ N$

We have 2 unknowns ($F_3$ and b) and we have 2 equations.  

Now we clear $F_3$ from the second equation and introduce it into the first equation.  

$F_3 = \frac{F_2}{cos (b)}$

Then

$-\frac{F_2}{cos (b)}sin(b)+F_1 = 0\\\\F_1 = \frac{F_2}{cos (b)}sin(b)\\\\F_1 = F_2tan(b)\\\\tan(b) = \frac{F_1}{F_2}\\\\tan(b) = \frac{5.7}{1.9}\\\\tan^{-1}(\frac{5.7}{1.9}) = b\\\\b= 72\°\\\\m = b +90\\\\\m= 162\°$

Then we find the value of $F_3$

$F_3 = \frac{F_1}{sin(b)}\\\\F_3 =\frac{5.7}{sin(72\°)}\\\\F_3 = 6.01 N$

So the answer is 6.3 N at 162° counterclockwise from  F1