Question

two forces p and q making an angle of 60degrees with each other at a point . p has magnitude of 8N and magnitude of resultant of two forces is root 84 N. then what will be the magnitude of theta?​

Answer 1

Given :

Magnitude of force p :

= 8 N

Angle between to forces p and q ;

= 60°

Magnitude of resultant of the two forces :

= $\sqrt{84}$

To Find :

Magnitude of resultant angle $\theta$ = ?

Solution :

∴We know the formula for resultant of the vectors p and q is :

$R=\sqrt{p^{2}+ q^{2}+ 2\times p \times q \times cos\alpha }$

where α is any angle between the two vectors .

So now putting the values in this equation we can get the value of q as :

$\sqrt{84} = \sqrt{8^{2} + q^{2} + 2\times 8\times q \times cos60 } \\\\84= 64 + q^{2} + 16 \times q \times \frac{1}{2} \\\\q^{2} + 8q - 20=0$

On solving this equation we get q:

= 2 N

Now for finding the value of $\theta$ we take the help of attached fig and proceed as :

$tan\theta= \frac{DR}{OD} \\\\\tan \theta=\frac{2\times sin60}{8+ 2\times cos 60}\\ \\tan \theta =\frac{\sqrt{3} }{8}$

$\theta= tan^{-1} \frac{\sqrt{3} }{8}$

So finally the magnitude of $\theta$ is $tan^{-1} \frac{\sqrt{3} }{8}$ .

Answer 2

Answer:

Given :

Magnitude of force p :

= 8 N

Angle between to forces p and q ;

= 60°

Magnitude of resultant of the two forces :

=  

To Find :

Magnitude of resultant angle  = ?

Solution :

∴We know the formula for resultant of the vectors p and q is :

where α is any angle between the two vectors .

So now putting the values in this equation we can get the value of q as :

On solving this equation we get q:

= 2 N

Now for finding the value of  we take the help of attached fig and proceed as :

So finally the magnitude of  is  .

Explanation: