Question

Find te equation of the line of action of the resultant of a system of coplanar forces

Answer 1

Answer:

The resultant is obtained by adding all the forces if they are acting in the same direction. If any one of the forces is acting in the opposite direction, then resultant is obtained by subtracting that force.

Answer 2

Answer:

The resultant R of the given forces will be given by the equation:

R = √ (∑V)2 + (∑H)2

Explanation:

The resultant force, of a given system of forces may be found out by the method of resolution as discussed below: Let the forces be P1, P2, P3, P4, and P5 acting at ‘o’. Let OX and OY be the two perpendicular directions. Let the forces make angle a1, a2, a3, a4, and a5 with Ox respectively. Let R be their resultant and inclined at angle θ. with OX Resolved part of ‘R’ along OX = Sum of the resolved parts of P1, P2, P3, P4, P5 along OX.

Resolve all the forces horizontally and find the algebraic sum of all the horizontally components (i.e., ∑H)

Rcosθ = P1cosα1 + P2cosα2 + P3cosα3 + P4cosα4 + P5cosα5 = X (Let)

Resolve all the forces vertically and find the algebraic sum of all the vertical components (i.e., ∑V)  

Rsin θ = P1sinα1 + P2sinα2 + P3sinα3 + P4sinα4 + P5sinα5 = Y (Let)

The resultant R of the given forces will be given by the equation:

R = √ (∑V)2 + (∑H)2

We get R2(sin2θ + cos2θ) = P12(Sin2α1+ cos2α1) + --- i.e.,

R2 = P12 + P22 + P32 + ---

And The resultant force will be inclined at an angle ‘θ’with the horizontal, such that tanθ = ∑V/∑H

Reference Link

• https://brainly.in/question/48351635