Question

calculate the angle between 2N force and 3N force so that their resultant is 4 n
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Answer 1

Answer:-

Given:

Magnitude of first force (A) = 2 N

Magnitude of second force (B) = 3 N

Magnitude of resultant force (R) = 4 N

We know that,

R² = A² + B² + 2AB cos θ

Where,

θ is the angle between the two forces.

So,

⟶ (4)² = (2)² + (3)² + 2 * 2 * 3 cos θ

⟶ 16 = 4 + 9 + 12 cos θ

⟶ 16 - 4 - 9 = 12 cos θ

⟶ 3 = 12 cos θ

⟶ 3/12 = cos θ

⟶ cos⁻¹ (1/4) = θ

⟶ 75.5° = θ (Approx.)

∴ The angle between the two forces is cos⁻¹ (1/4) ≈ 75.5°.

Answer 2

Answer:

☆ Given :-

• The angle between 2 N force and 3 N force so that their resultant is 4 N.

☆ To Find :-

• What is the angle between two forces.

☆ Formula Used :-

✪ R² = A² + B² + 2AB cos $\theta$ ✪

☆ Solution :-

Let, the two vectors be A and B and their resultant be R.

Let, the angle between A and B is $\theta$

⋆ Given :-

• A = 2 N
• B = 3 N
• R = 4 N

✳ According to the question by using the formula we get,

⇒4² = 2² + 3² + 2 ×2 ×3 cos$\theta$

⇒16 = 4 + 9 + 12 cos$\theta$

⇒16 - 4 - 9 = 12 cos$\theta$

⇒3 = 12 cos$\theta$

⇒$\sf\dfrac{\cancel{3}}{\cancel{12}}$ = cos$\theta$

⇒cos$\theta$ = $\dfrac{1}{4}$

➙ $\theta$ = cos-¹($\dfrac{1}{4}$)

$\therefore$ The angle between the two forces is cos-¹($\dfrac{1}{4}$)

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