Question
Two force 10N and 20N are inclined at angle 60° to each other find the resultant.make use of parallelogram method
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GPT-5 mini
Using the parallelogram method (diagonal of the parallelogram formed by the two force vectors):
Let the 20 N force lie along the x-axis and the 10 N force be inclined at 60° above it.
1. Magnitude (by the cosine law)
R = sqrt(10^2 + 20^2 + 2·10·20·cos60°)
= sqrt(100 + 400 + 400·0.5)
= sqrt(700) = 10√7 ≈ 26.46 N.
2. Direction (angle φ of R above the 20 N force)
Resolve components:
Rx = 20 + 10 cos60° = 20 + 5 = 25
Ry = 10 sin60° = 10·(√3/2) = 5√3 ≈ 8.6603
φ = arctan(Ry / Rx) = arctan((5√3)/25) = arctan(√3/5) ≈ 19.1°.
Answer: Resultant = 10√7 N ≈ 26.46 N, directed 19.1° above (toward the 10 N force from) the 20 N force.
Let the 20 N force lie along the x-axis and the 10 N force be inclined at 60° above it.
1. Magnitude (by the cosine law)
R = sqrt(10^2 + 20^2 + 2·10·20·cos60°)
= sqrt(100 + 400 + 400·0.5)
= sqrt(700) = 10√7 ≈ 26.46 N.
2. Direction (angle φ of R above the 20 N force)
Resolve components:
Rx = 20 + 10 cos60° = 20 + 5 = 25
Ry = 10 sin60° = 10·(√3/2) = 5√3 ≈ 8.6603
φ = arctan(Ry / Rx) = arctan((5√3)/25) = arctan(√3/5) ≈ 19.1°.
Answer: Resultant = 10√7 N ≈ 26.46 N, directed 19.1° above (toward the 10 N force from) the 20 N force.