Question

the sum of they magnitude of 2 force act a point is 18 and the magnitude of the resultant is 12 if the resultant is add 90 degree with the force of smaller magnitude what are the magnitude of force​

Answer 1

Answer:-

Given:

Sum of magnitudes of two forces = 18 N

Magnitude of resultant (R) = 12 N

Angle between Resultant and smaller force = 90°.

Let the magnitude of the two forces be A & B (A > B).

⟶ A + B = 18

⟶ A = 18 - B

We know that,

• R² = A² + B² + 2AB cos ∅

where ∅ is the angle between A , B.

According to the question,

⟶ A² = R² + B² + 2RB cos 90°

(since, Angle between R & B is 90° )

Substitute the value of A from equation (1)

• cos 90° = 0

⟶ (18 - B)² = (12)² + B²

• (a - b)² = a² + b² - 2ab

⟶ (18)² + B² - 36B = 144 + B²

⟶ 324 - 144 = 36B

⟶ 180/36 = B

⟶ 5 N = B

Substitute the value of B in equation (1).

⟶ A = 18 - 5

⟶ A = 13 N

∴ Magnitudes of two forces are 13 N , 5 N

Answer 2

Answer:

Given :-

• The sum of the magnitude of 2 force act point 18 and the magnitude of the resultant is 12. If the resultant is add 90° with the force of smaller magnitude.

To Find :-

• What is the magnitude of force.

Solution :-

$\mapsto$ Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.

$\mapsto$ As the resultant force makes 90° with the smaller force P then Q forms the hypotenuse of the triangle.

▪️ We can written as,

$\leadsto$ Q² - P² = R²

$\implies$ Q² - P² = (12)²

$\implies$ Q² - P² = 144 .... Equation no (1)

The sum of magnitude of two forces is given as,

$\implies$ P + Q = 18

$\implies$ Q = 18 - P .... Equation no (2)

$\Rightarrow$ Substituting the value from the equation no (2) in equation no (1) we get,

$\implies$ (18 - P)² - P² = 144

$\implies$ P = 5 N

$\Rightarrow$ Substituting the value of P in the equation no (1) we get,

$\implies$ Q = 18 - 5

$\implies$ Q = 13 N

$\therefore$ The magnitude of two forces is $\boxed{\bold{\large{5\: N}}}$ and $\boxed{\bold{\large{13\: N}}}$

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