Engineering Mechanics

Chapter 2 : Composition and Resolution of Forces „„„„„ 17

∴

22

22

0.866 0.866

0.577

40 – 0.5 40 – 0.5

FF

FF

×

==

×

2

22

0.866

40–0.5 1.5

0.577

F

FF==

∴ 2 F 2 = 40 or F 2 = 20 Ans.

Example 2.3. Find the magnitude of the two forces, such that if they act at right angles, their

resultant is 10 N. But if they Act at 60°, their resultant is 13 N.

Solution. Given : Two forces = F 1 and F 2.

First of all, consider the two forces acting at right angles. We know that when the angle between

the two given forces is 90°, then the resultant force (R)

22

10 =+FF 12

or 10 =+FF 1222 ...(Squaring both sides)

Similarly, when the angle between the two forces is 60°, then the resultant force (R)

22

13 =++FF FF12 12 2 cos 60°

∴ 13 =++FF FF12 12^222 ×0.5 ...(Squaring both sides)

or F 1 F 2 = 13 – 10 = 3 ...(SubstitutingFF 1222 +=10)

We know that (F 1 + F2])^2 = FF FF12 12^22 ++ 210616 =+=

∴ FF 12 += = 16 4 ...(i)

Similarly (– )FF F F FF 12222 =+1 2 12–2 =10–64=

∴ FF 12 –42== ...(ii)

Solving equations (i) and (ii),

F 1 = 3 N and F 2 = 1 N Ans.

2.12.RESOLUTION OF A FORCE

The process of splitting up the given force into a number of components, without changing its
effect on the body is called resolution of a force. A force is, generally, resolved along two mutually
perpendicular directions. In fact, the resolution of a force is the reverse action of the addition of the
component vectors.

2.13.PRINCIPLE OF RESOLUTION

It states, “The algebraic sum of the resolved parts of a no. of forces, in a given direction, is
equal to the resolved part of their resultant in the same direction.”

Note : In general, the forces are resolved in the vertical and horizontal directions.