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Two forces 3p, 2p have a resultant R. If the first force is doubled, the magnitude of the resultant is also doubled. Find the angle between the forces.

Two forces 3p, 2p have a resultant R. If the first force is doubled, the magnitude of the resultant is also doubled. Find the angle between the forces.

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
2 years ago
We have ,

R^2=(3P)^2+(2P)^2+2(3P)(2P)cos\theta
\implies R^2=13P^2+12P^2cos\theta

Now the first foce is doubled and so does the resultant.

\implies (2R)^2=(6P)^2+(2P)^2+2(6P)(2P)cos\theta
\implies 4R^2=40P^2+24P^2cos\theta

Solving the two equations gives

cos\theta=-\dfrac{1}{2}\implies \theta=120^{\circ}

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