Question

find the resultant of two forces equal to 3 Newtons and 6 Newton respectively
acting at an angle of 120 degree​

Answer 1

Answer :-

3√3 N

Given :-

• Forces acting on the body are 3N , 6N
• Angle between them is 120°

To find :-

• Resultant force

Solution :-

As we know the formula to find the resultant forces that is

$\red {\dag \: F_r = \sqrt{F_1 {}^{2} +F_2 {}^{2} + 2 F_1F_2cos \theta} }$

• F1 ,F2 are forces acting on the body
• Fr resultant force

Substituting the values,

${ \: F_r = \sqrt{(3) {}^{2} +(6) {}^{2} + 2 (3)(6)cos 120 {}^{ \circ} } }$

As we know that cos120° is -1/2

Simplifying the values

${ \: F_r = \sqrt{9 +36 + 2 (3)(6) \bigg(\dfrac{ - 1}{2} \bigg) } }$

${ \: F_r = \sqrt{9 +36 + 36 \bigg(\dfrac{ - 1}{2} \bigg) } }$

${ \: F_r = \sqrt{9 +36 + \dfrac{ - 36}{2} } }$

${ \: F_r = \sqrt{45 - 18 } }$

${ \: F_r = \sqrt{27 } }$

$\red { \: F_r =3 \sqrt{3 } }$

So, the resultant force is 3√3 N

Know more similar question in brainly:-

brainly.in/question/41072528

Answer 2

Answer :-

3√3 N

Given :-

Forces acting on the body are 3N , 6N

Angle between them is 120°

To find :-

Resultant force

Solution :-

As we know the formula to find the resultant forces that is

$\red {\dag \: F_r = \sqrt{F_1 {}^{2} +F_2 {}^{2} + 2 F_1F_2cos \theta} }$

F1 ,F2 are forces acting on the body

Fr resultant force

Substituting the values,

${ \: F_r = \sqrt{(3) {}^{2} +(6) {}^{2} + 2 (3)(6)cos 120 {}^{ \circ} } }$

As we know that cos120° is -1/2

Simplifying the values

${ \: F_r = \sqrt{9 +36 + 2 (3)(6) \bigg(\dfrac{ - 1}{2} \bigg) } }$

${ \: F_r = \sqrt{9 +36 + 36 \bigg(\dfrac{ - 1}{2} \bigg) } }$

${ \: F_r = \sqrt{9 +36 + \dfrac{ - 36}{2} } }$

${ \: F_r = \sqrt{45 - 18 } }$

${ \: F_r = \sqrt{27 } }$

$\red { \: F_r =3 \sqrt{3 } }$

So, the resultant force is 3√3 N

Know more similar question in brainly:-

brainly.in/question/41072528