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+1 vote
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in Physics by (66.1k points)

The angle between the two forces of magnitude 20KN and 15KN is 60º, the 20KN force being horizontal. Determine the resultant in magnitude and direction if 

(i) the forces are pulls 

(ii) the 15KN force is push and 20KN force is a pull

1 Answer

+2 votes
by (58.2k points)
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Best answer

Since there are two forces acting on the body, So we use Law of Parallelogram of forces.

Case-1: P =20 KN, Q = 15KN, α = 60°

R2 = P2 + Q2 + 2PQ cosα = 202 + 152 + 2 × 20 × 15 cos 60° 

R = 30.41KN

tanθ = Q sinα/(P + Q cosα) = 15 sin 60°/(20 + 15 cos 60°)

θ = 25.28º

Case-2: Now angle between two forces is 120º, P = 20KN, Q = 15KN, α =120°

R2 = P2 + Q2 + 2PQ cosα = 202 + 152 + 2 × 20 × 15 cos 120°

R = 18.027KN

tanθ = Q sinα/(P + Q cosα) = 15 sin 120°/(20 + 15 cos 120°)

θ = –46.1º.

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