Solved Example & Practice Problems: Resolution and Composition of Forces: Rectangular Components

Solved Examples for Understanding

Example 2.4.1 

Find x and y components of the 6 forces shown in Fig. 2.4.1. Also write the forces in terms of unit vector î and ĵ along x and y directions respectively.

Solution: 

Example 2 4.2 

Find x and y components of the forces shown in Fig. 2.4.2.

Solution: 

When slopes are given for the forces, their angles with horizontal can be obtained using

Example 2.4.3 

Find the x and y components of a 1000 N force acting from the point (-3, 5) of a 1000 N force acti towards the point (6. – 3).

Solution: 

The angle of the force with horizontal can be calculated by plotting it as shown in Fig. 2.4.3.

Example 2.4.4 

Find the magnitude and direction of forces having x and y components as shown in Fig. 2.4.4 (a) to (d).

Solution: For Fig. 2.4.4 (a),

Example 2.4.5 

Find components Fa and Fb of the 100 N force along the directions shown in Fig. 2.4.5 using rectangular components.

Solution:  

• As 100 N force is being resolved into components Fa and Fb the 100 N force will be a resultant of Fa and Fb.

• For rectangular components, X and Y directions are required which can be chosen according to convenience.

• Let X-axis be along the 100 N force and Y-axis perpendicular to it as shown in Fig. 2.4.5 (a).

Example 2.4.6 

Determine the resultant of the five forces shown in Fig. 2.4.6.

Solution : 

Resolving forces in X and Y directions,

Example 2.4.7 

If the resultant of the two forces shown in Fig. 2.4.7 is 700 N directed vertically upwards, find the angles a and B using rectangular components.

Solution: 

Choosing X-axis horizontal and Y-axis vertical.

As resultant is vertical, its x component is 0 and y component is 700 N.

25 = 16+ 49 - 56 cos β

56 cos β = 40

Examples for Practice

Q.1 

A force F1 = 1200 N is acting vertically on an incline [Refer Fig. 2.4.8]. Find its components along X and Y axes.

[Ans.: F1x = -720N, F1y = -960N]

Q.2

A force of 200 N is acting on a block as shown in Fig. 2.4.9. Find the component of force along the horizontal and vertical axis.

[Ans.: Fx = 100 N, Fy = 173.2.N]

Q.3

Find x and y components of forces shown in Fig. 2.4.10.

 [Ans.: F1x = -150N, F1y = 200N

F2x = 89.44 N, F2y =178.89 N, F3x = -60N, F3y = 80N]

Q.4

Determine the x and y components of a force of magnitude 50 N acting from point A(1,4) towards B(- 2, 8). Also write the force vector in terms of unit vectors along x and y direction. 

[Ans. : Fx = -30 N, Fy = 40 N, ]

Q.5

Determine the magnitude and direction of the forces having x and y components given below:

Q.6

Determine components Fa and Fb of the 500 N force along the directions shown in Fig. 2.4.11. using rectangular components.

 [ Ans. : Fa = 442.28 N, Fb = 542.53 N]

Q.7

Find the resultant of coplanar concurrent force system shown in Fig. 2.4.12.

[Ans. : R = 459.8 N, 51.24° ]

Q.8

If the resultant of the two forces shown in Fig. 2.4.13. is 90 kN directed vertically upwards, find the angles α and β using rectangular components.

[Ans. : α = 39.29°, β = 56.44°]