Forces in
Equilibrium
and direction
Vector is a
physical quantity that has both
magnitude .
Scalar is a
physical quantity that has
magnitude only .
The force F can be resolved into 2
perpendicular components .
↳ F O of action of force
cos
parallel to line at
angle -0 to the line the
:
a .
F
perpendicular to the line
↳
sin Q :
.
If two forces which act point object
are
equal and
opposite to each other on a
,
the
object is in
equilibrium .
↳ resultant of the two forces is zero .
↳ the two forces are balanced .
forces act resultant of
When 3 on a
point object ,
resultant -
- O
only
if the
any
two
forces and to force
is
equal opposite the third .
Resolve force
each and
perpendicular
↳
along the same
parallel .
↳ Balance the
components along each line .
The moment of force
force the
perpendicular distance from the line of action
•
a is x
of the force to the point .
Principle of moments States that for
system equilibrium
•
a in
,
sum of clockwise moments =
sum of anticlockwise moments
Centre of effect
mass is the
point through which
single force the
body has
turning
•
a on no .
Moment = F x d
, Sz
S
^
d. da = W t W t
Wo
< ,, , z
,
•
-
' W d
, ,
=
Wzdz
v pivot
V v
W,
Wo W2
S .
^
Sy
n
d. I dy
Moments about X :
Moments about Y : e
Y
'
i
Wdx S D=
Syd Wdy
=
..
w
Wdsc S =
Wdy pillar pillar
Y
Sy
= ,,
D se
D
L S
D
A of and forces
couple equal opposite acting body but not
along line
•
the
is a
pair on a
,
same .
Moment force action forces
of couple perpendicular distance between lines of of the
°
:
a x .
F Fa t F Ld -
x ) =
Fx + Fd -
Fx
^
x d -
x = Fd
( K 7
•
The total moment the of the
p
is same
, regardless
F about which the taken
point moments
< x are .
d
An stable released
object in
equilibrium will return to its
equilibrium position if
displaced then .
If an
object in unstable
equilibrium is
displaced ,
the displacement will increase
,
causing
the
object to be further from the
equilibrium position .
tilted too far
For to
For
tilting to occur
,
toppling occur
,
b
line of action of
< , Fd >
wzb weight
F s - - -
a-
-
•
passes beyond the
pivot
d
•
VW
v .
p
•
✓
p
w
Vector of of forces 0
sum
triangle F Fa Fs
: =
t t
,
Conditions of of
equilibrium body I Resultant force must be
:
a .
zero .
2 .
Principle of moments must
apply .
Equilibrium
and direction
Vector is a
physical quantity that has both
magnitude .
Scalar is a
physical quantity that has
magnitude only .
The force F can be resolved into 2
perpendicular components .
↳ F O of action of force
cos
parallel to line at
angle -0 to the line the
:
a .
F
perpendicular to the line
↳
sin Q :
.
If two forces which act point object
are
equal and
opposite to each other on a
,
the
object is in
equilibrium .
↳ resultant of the two forces is zero .
↳ the two forces are balanced .
forces act resultant of
When 3 on a
point object ,
resultant -
- O
only
if the
any
two
forces and to force
is
equal opposite the third .
Resolve force
each and
perpendicular
↳
along the same
parallel .
↳ Balance the
components along each line .
The moment of force
force the
perpendicular distance from the line of action
•
a is x
of the force to the point .
Principle of moments States that for
system equilibrium
•
a in
,
sum of clockwise moments =
sum of anticlockwise moments
Centre of effect
mass is the
point through which
single force the
body has
turning
•
a on no .
Moment = F x d
, Sz
S
^
d. da = W t W t
Wo
< ,, , z
,
•
-
' W d
, ,
=
Wzdz
v pivot
V v
W,
Wo W2
S .
^
Sy
n
d. I dy
Moments about X :
Moments about Y : e
Y
'
i
Wdx S D=
Syd Wdy
=
..
w
Wdsc S =
Wdy pillar pillar
Y
Sy
= ,,
D se
D
L S
D
A of and forces
couple equal opposite acting body but not
along line
•
the
is a
pair on a
,
same .
Moment force action forces
of couple perpendicular distance between lines of of the
°
:
a x .
F Fa t F Ld -
x ) =
Fx + Fd -
Fx
^
x d -
x = Fd
( K 7
•
The total moment the of the
p
is same
, regardless
F about which the taken
point moments
< x are .
d
An stable released
object in
equilibrium will return to its
equilibrium position if
displaced then .
If an
object in unstable
equilibrium is
displaced ,
the displacement will increase
,
causing
the
object to be further from the
equilibrium position .
tilted too far
For to
For
tilting to occur
,
toppling occur
,
b
line of action of
< , Fd >
wzb weight
F s - - -
a-
-
•
passes beyond the
pivot
d
•
VW
v .
p
•
✓
p
w
Vector of of forces 0
sum
triangle F Fa Fs
: =
t t
,
Conditions of of
equilibrium body I Resultant force must be
:
a .
zero .
2 .
Principle of moments must
apply .
