Question

The angle between two forces of equal magnitude is 60°, and the magnitude of their resultant is 71√3 N. What is the magnitude of the forces?​

Answer 1

Answer:

F=71N

Explanation:

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Answer 2

Answer:

$\footnotesize{ \maltese \: \underline{ \underline{ \sf | \overrightarrow{F} | = 71 \sqrt{3} \: N } }}\: \maltese$

Angle between the two forces is given as : 60°

$\longrightarrow\:\sf R = \sqrt{F^2 + F^2 + 2 F.F \cos (\theta)}$

• R = resultant of 2 the two forces
• θ = angle between the two forces

$\longrightarrow\:\sf 71 \sqrt{3} = \sqrt{2F^2 + 2 F^{2} \cos (6 {0}^{ \circ} )}$

$\longrightarrow\:\sf 71 \sqrt{3} = \sqrt{2F^2 + 2 F^{2} \times \dfrac{1}{2} }$

$\longrightarrow\:\sf 71 \sqrt{3} = \sqrt{2F^2 + F^{2} }$

$\longrightarrow\:\sf 71 \sqrt{3} = \sqrt{3 F^{2} }$

$\longrightarrow\:\sf 71 \sqrt{3} = \sqrt{3 } F$

$\longrightarrow\:\underline{\underline{\sf F = 71 \:N}}$