Question

two equal forces 121.3N when they are inclined at an angle 120 degree then the resultant force will be

Answer 1

SOLUTION

GIVEN

Two equal forces 121.3 N when they are inclined at an angle 120°

TO DETERMINE

The resultant force

EVALUATION

Here it is given that two equal forces 121.3 N when they are inclined at an angle 120°

First force = A = 121.3 N

Second force = B = 121.3 N

Angle = θ = 120°

Hence the required resultant force

$\sf{ = \sqrt{ {A}^{2} + {B}^{2} + 2AB \cos \theta} }$

$\sf{ = \sqrt{ {(121.3)}^{2} + {(121.3)}^{2} + 2 \times 121.3 \times 121.3 \times ( - \frac{1}{2}) } }$

$\sf{ = \sqrt{ {(121.3)}^{2} + {(121.3)}^{2} - {(121.3)}^{2} } }$

$\sf{ = \sqrt{ {(121.3)}^{2} } }$

$\sf{ = 121.3 }$

FINAL ANSWER

Hence the required resultant force = 121.3 N

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Answer 2

Given:

Two equal forces 121.3N when they are inclined at an angle 120°.

To find:

Resultant force ?

Calculation:

Resultant value of force is given as :

$\boxed{ \sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \theta) } }$

Now, since forces are equal, applying the values:

$\sf \implies R = \sqrt{ {a}^{2} + {a}^{2} + 2 {a}^{2} \cos( \theta) }$

$\sf \implies R = \sqrt{2 {a}^{2} + 2 {a}^{2} \cos( \theta) }$

$\sf \implies R = \sqrt{2 {a}^{2} \{1+ \cos( \theta) \} }$

$\sf \implies R = \sqrt{4{a}^{2} { \cos}^{2} ( \frac{ \theta}{2} )}$

$\sf \implies R =2a \cos( \frac{ \theta}{2} )$

Putting necessary values:

$\sf \implies R =2 \times 121.3 \cos( \frac{ {120}^{ \circ} }{2} )$

$\sf \implies R =2 \times 121.3 \cos( {60}^{ \circ} )$

$\sf \implies R = 121.3 \: N$

So, resultant is 121.3 N