Addition of Coplanar Forces – Using Scalar Notation

For problems and solutions on addition of coplanar forces click HERE.

Given the coplanar forces F₁, F₂ and F₃ below, find the resultant force F_R = F₁ + F₂ + F₃

 

Step 1:

Resolve the forces into their rectangular components i.e.:

Step 2:

Determine the resultant force in the x-axis and y-axis independently i.e.:

Step 3:

Finally determine the magnitude of the resultant force F_R and its direction θ :

 

For problems and solutions on addition of coplanar forces click HERE.

 

Coplanar Forces and their Rectangular Components

Coplanar forces: a set of forces is coplanar if they all lie in the same geometric plane.  In the diagram below forces F₁, F₂ and F₃ are coplanar because the all lie in the x-y plane.  Refer to the image below.

Coplanar forces can be resolved into components along the x and y axes.  These component forces are called rectangular components.  Rectangular components can be represented in two ways:

1. Scalar notation
2. Cartesian vector notation

Scalar Notation: When using the scalar notation the rectangular components of force F is written F_x and F_y.

• F_x represents the component in the x-axis
• F_y represents the component in the y-axis

Refer to the image below.

 

Cartesian Vector Notation: When using the Cartesian vector notation, the rectangular components are represented in terms of unit vectors i and j.  Unit vectors are vectors that have a magnitude of one and they are used to represent direction.  In this case:

• i represents direction in x-axis
• j represents direction in y-axis

Refer to the image below.