Motion in a plane

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Question

The greatest and least resultant of two forces are 7 N and 3 N respectively. If each of the force is increased by 3 N and applied at 60°. The magnitude of the new resultant is

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Solution

P + Q = 7 N ; P – Q = 3 N
P = 5 N, Q = 2 N
$∴$ P¹ = 8 N, Q¹ = 5 N, θ = 60⁰

${R^1} = \sqrt {{{(8)}^2} + {{(5)}^2} + 2 X 8 X 5 \times \frac{1}{2}}$

$= \sqrt {64 + 25 + 40} = \sqrt {129} N$

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