PHYSICS:RESOLUTION OF VECTORS

Resolution of Vectors

The Concept of Components of a Vector

Explain the concept of components of a vector

Is the Splits or separates single vector into two vectors (component vectors) which when compounded, provides the resolved vector.

Resolved vector is asingle vector which can be split up into component vectors.

Component vectorsare vectors obtained after spliting up or dividing a single vector.

Resolution of a Vector into two Perpendicular Components

Resolve a vector into two perpendicular components

Components of a vector are divided into two parts:

1. Horizontal component
2. Vertical component

Take angle OAC

Case 1

SinQ = FX/F

Thus

FX = F SinQ

Horizontal component, FX = FSinQ

Case 2

Cos Q = Fy/F

Thus:

Fy = FCosQ

Vertical component: Fy = FCosQ

Resolution of Vectors in Solving Problems

Apply resolution of vectors in solving problems

Example 8

Find the horizontal and vertical components of a force of 10N acting at 30⁰ to the vertical.

Solution

FX = FCOS 60º

Since

Cos 60º /F =(FX)

FX = F CoS60º _________________(1)

FX = 10NCos 60º

Fy = ?

Sinq = Fy

Fy =F SinQ __________________________ (ii)

Fy= 10N Sin 60º