Page 153 - WCS - Electrical

P = BC Q.Sin θ
Q
WORKSHOP CALCULATION & SCIENCE - CITS AC tan α = P + Q.cos θ
P
P = BC = BC tan Q.Sin Q.Sin θ
θ
α =
Q
Q.Sin
P +
Q AC AC BCP Q× BC P = BC tan α = P + Q.cos Q.cos θ θ
θ
AC = =
P×
Q AC Q AC tan α = P + Q.cos θ covered

Distance
P
BC
P× AC = Q× P BC BC = QxBC Speed =
P× AC = Q× BC = P Q = AC BCP Time

AC
Q
P× AC = Q× BC AC= AC Speed = Distance covered
Distance
covered

Q

Time
QxBC QxBC PxAC Speed = Speed = Distance covered direction
Time
Distance
Definite

P =

P = ACP = Velocity =
AC P = QxBC Time Time
BC
AC
Distance

PxAC

Definite

PxAC
Distance
direction

The State (mutual intersecting forces). When two or more forces act on a point while intersecting each other Definite direction
Velocity =
P =
Velocity =
P =

Distan

BC PxAC

CD
BC
Tim
their resultant force acts on the same point. This is worked out on the principles of parallelogram, triangulation or e Time Definite ce direction
Sin
P =
Velocity =
θ =
velocity
polygonal forces. BC Q a = change in Time m/sec 2

Time
Sin CD
Space diagram Sin θ = θ = CD CD BD change in velocity
θ =
Cos
Q

Q
Q
a =
Sin
θ =
2
This diagram indicates the line of action and the direction of force. a = change in velocity m/sec m/sec 2 2
ch

Q
Time in ange
velocity

BD
a =
Cos BD
Vector diagram Cos θ = θ = Time Time 1 m/sec
Q

Q R = θ Cos = BD 2 2.P.Q cos θ 2
2
Q +
P +
In this diagram taking a scale the quantity of force and the direction are indicated. Such as 1 1
Q
Suppose 10 kg = 1 cm R = P + Q + 2.P.Q cos θ CD 2 2 1
2
2
CD
2
2
R = P + Q + 2.P.Q cos θ =  (v −u) 
tan
α =
2
50 kg = 5 cm R = P + Q 2 OD 2.P.Q+ OB + θ cos BD F = m 2   t  

CD
tan CD
= CD
70 kg = 7 cm tan α = α = = OD CD CD BD θ CD F = m F  ( = m −u)v  (v −u)  
 

OB +

Q.Sin

BD
OD
OB +
=
t
tan
= =
α

From a point Q,, a 7 cm line segment O, B, is drawn parallel to OB and a 5 cm line segment O, A, is drawn parallel  mF   = t  (v −u)  
θ BD
Q.cos +
OD
OB
P +
to OA, then A, O, B, is called vector diagram and AOB is called space diagram  t 
θ

Q.Sin
Q.Sin θ
=
=
P +
θ
Q.Sin
If at point 50 kg and 70 kg, two forces are acting at an angle of 45° from each other, then their space diagram and
Q.cos
θ

Q.Sin
θ
Q.cost
α
θ an =
P +
vector diagram will be prepared as = P + Q.cos Q.cos θ
P +
θ
Representation of Force tan Q.Sin Q.Sin θ
θ
α =
tan α = P + Q.cos θ θ
Q.Sin
Q.cos
θ
P +
tan
α =
In the force, there is both magnitude and direction. This isindicated by a straight line with an arrow marked ahead.

2
2
Q.cos
θ
P +

cos
2.P.Q
P +
Q +
R =
θ
The length of the straight line is the magnitude of force andthe arrow mark shows the direction. Such as if any
force acts from O to B then it is indicated by the arrow OB and a if the same force is acting from O to A then this

2
2
Q +
P +
will be indicated by the sign, OA. R = R = Q + 2.P.Q 2.P.Q θ cos θ
2
2

cos
P +

2
2
Parallel Forces R = P + Q + 2.P.Q cos θ
When forces simultaneously act on a body and their directions are parallel to each other, then they are called a
parallel forces. If the direction of parallel forces is the same ,they are called like parallel forces and in case they
act in opposite direction, they are called unlike parallel forces.
Couple
A pair of two equal and unlike parallel forces i.e., force equal in magnitude, with lines of action parallel to each
other and acting in opposite directions is known as couple.
As a matter of fact, a couple is unable to produce any translatory motion i.e., motion in a straight line. But it
produces a motion of rotation in the body, on which it acts.
The simplest example of a couple is the forces applied to key of a lock, while locking or unlocking it.
140
CITS : WCS - Electrical - Exercise 13