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Svetach [21]
3 years ago
11

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 wil

l 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

Physics
1 answer:
Lilit [14]3 years ago
4 0

Answer:

Second option 6.3 N at 162° counterclockwise from  F1

Explanation:

<u><em>Observe the attached image</em></u>. 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

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