Question

If the resultant of two forces of magnitude p and 2p is perpendicular to p then the angle between the forces

Answer 1

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Answer 2

Answer:

The angle between the forces is 120°.

Explanation:

Given that,

First vector = P

Second vector = 2P

Let R be the magnitude of resultant.

Let Ф be the angle between R and 2P.

Using cosine rule

The magnitude of resultant P and 2P is

$R=2p\cos\theta$

Now,

$R^2=P^2+(2P)^2+2\times P\times 2P\cos(90+\theta)$

$4P^2\cos^2\theta=P^2+4P^2+4P^2-\sin\theta$

$4\cos^2\theta=5-4\sin\theta$

$4(1-\sin^2\theta)=5-4\sin\theta$

$4\sin^2\theta-4\sin\theta+1=0$

$(2\sin\theta-1)^2=0$

$2\sin\theta=1$

$\theta = sin^{-1}\dfrac{1}{2}$

$\theta=\dfrac{\pi}{6}=30^{\circ]$

The angle between the forces is

$\alpha=90^{\circ}+\theta$

$\alpha=90+30$

$\alpha=120^{\circ}$

Hence, The angle between the forces is 120°.