Question

What is the angle between two forces F1=2N and F2=3N having resultant as 4N​

Answer 1

Explanation:

it is based on the resultant of two vectors I have written that formula. here the theta is the angle between the two vectors

Answer 2

Given :

Resultant of two forces = 4N

F₁ = 2N

F₂ = 3N

To find :

The angle between two forces.

Solution :

Using law of cosine that is,

If two vectors A and B of magnitudes A and B are acting at an angle θ, then the magnitude of their resultant using parallelogram method of vector addition is,

$\boxed{ \sf R = \sqrt{ A^2 + B^2 + 2ABcos \theta}}$

By substituting the values,

$\dashrightarrow\sf R = \sqrt{ F_1^{2} + F_2 ^{2} + 2ABcos \theta}$

$\dashrightarrow\sf 4 = \sqrt{2^{2} + 3 ^{2} + 2(2)(3)cos \theta}$

$\dashrightarrow\sf 16 = 4 + 9 + 12cos \theta$

$\dashrightarrow\sf 16 = 13 + 12cos \theta$

$\dashrightarrow\sf 16 - 13 = 12cos \theta$

$\dashrightarrow\sf 12cos \theta = 3$

$\dashrightarrow\sf cos \theta = \dfrac{3}{12}$

$\dashrightarrow\sf cos \theta = \dfrac{1}{4}$

$\dashrightarrow\sf \theta = 75 \degree32'$

Thus, the angle between two forces is 75° 32'