Question

the sum of 2 forces inclined to each other at an angle is 18 kg wt and their resultant which is perpendicular to the smaller force is 12 kg wt. find the forces and the angle between them, right now just help me find the angle, pls I will mark the correct answer brainliest

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Answer 1

The second law of motion states that the force is a physical quantity which is defined as the rate of change of linear momentum with respect to the time and for a constant mass, it is the product of the mass and the acceleration.

Answer and Explanation:

F

1

+

F

2

=

18

N

(

F

1

+

F

2

)

2

=

324

F

2

1

+

F

2

2

=

324

−

2

F

1

F

2

Also, resultant is given by

R

=

√

F

2

1

+

F

2

2

+

2

F

1

F

2

cos

θ

144

=

324

−

2

F

1

F

2

cos

θ

+

2

F

1

F

2

cos

θ

2

F

1

F

2

(

1

−

cos

θ

)

=

180

Also,

tan

β

=

F

1

sin

θ

F

2

+

F

1

cos

θ

tan

90

∘

=

F

1

sin

θ

F

2

+

F

1

cos

θ

1

0

=

F

1

sin

θ

F

2

+

F

1

cos

θ

F

2

+

F

1

cos

θ

=

0

F

1

=

−

F

2

cos

θ

Substitute the value of

F

1

in equation (i),

F

2

=

√

90

cos

θ

(

cos

θ

−

1

)

Substituting

F

2

in the equation (i),

F

1

=

−

√

90

cos

θ

(

cos

θ

−

1

)