Question

find the angle between two equal forces P when their resultant is equal to P/2

Answer 1

Answer:

angle = cos^-1 [-7/8]

Explanation:

here

2 p^2 + 2p^2cos ø = p^2/4

Answer 2

The angle between two equal forces is 151.04 degrees.

Explanation:

The resultant of two vectors is given by :

$R=\sqrt{v_1^2+v_2^2+2v_1v_2\ \cos\theta}$

Here resultant is P/2 and two equal forces are P. So,

$\dfrac{P}{2}=\sqrt{P^2+P^2+2P^2\ \cos\theta}$

$\dfrac{P}{2}=\sqrt{2P^2+2P^2\ \cos\theta}$

$\dfrac{1}{2}=\sqrt{2+2\ \cos\theta}$

Squaring both sides we get :

$\dfrac{1}{4}=2+2\ \cos\theta$

$8\ \cos\theta=-7$

$\theta=\cos^{-1}(\dfrac{-7}{8})$

$\theta=151.04^{\circ}$

So, the angle between two equal forces is 151.04 degrees.

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