STABILITY OF FLOATING BODIES
(p.63)
LEARNING UNIT OUTCOMES
 Consider the equilibrium of the floating and
submerged bodies
 Define:
 Buoyancy force
 Center of buoyancy
 Metacenter
 Metacentric height
 Consider conditions of equilibrium of floating
and submerged body
SUBMERGED OBJECT
DEFINITION
 When a stationary body is completely submerged in a
fluid or floating so that it is only partially submerged, it is
subjected to an upward force that tends to lift it up. This
tendency for an immersed body to be lifted up in the fluid
due to an upward force opposite to the action of gravity is
known as buoyancy.
 The force that tends to lift the body is called the buoyancy
force
BUOYANCY FORCE
BUOYANCY
Submerged portion (yellow)
Displaced fluid whose volume =
yellow volume
LIQUID
BOUYANCY FORCE
=
WEIGHT OF DISPLACED FLUID
FOR THE BODY TO FLOAT:
R W
gVdf  Mg
gbxL  Mg
d
x
BG 

2 2
EXERCISE:
Meyer. Page 74. No.:4.1 – 4.4.
Douglas Part 1. Page 68. No.: 1, 2, 3, 4, 5.
BUOYANCY
This cargo ship has a uniform weight distribution and it is empty, as
noticed by how high it floats in the water relative to the top of the
boundary
STABILITY OF FLOATING BODIES
ARCHIMEDES LAW
THE BOYANCY FORCE ACTING UPWARDS ON
A FLOATING BODY = WEIGHT OF THE
DISPLACED VOLUME OF FLUID. THE
BUOYANCY FORCE IS ACTING THROUGH THE
CENTRE OF BUOYANCY (B) ON THE BODY.
b
M
W
d
x
G
Fluid
B
R
STABILITY OF FLOATING BODIES
Angular displacement
M
W
Fluid
G
B
x
R
Metacentre is the point at which the line of action of the force of
buoyancy will meet the normal axis of the body when the body is given
a small angular displacement (M).
Metacentric height is the distance between the metacentre of a floating
body and the centre of gravity of the body (MG).
STABILITY OF FLOATING BODIES
Angular displacement
M
W
Fluid
R W
G
gVdf  Mg
B
x
R
GM  BM  BG
gbxL  Mg
d
x
BG 

2 2
TYPES OF EQUILIBRIUM OF A FLOATING BODY
STABLE EQUILIBRIUM- A body is said to be in a stable
equilibrium, if it returns back to its original position when given a
small angular displacement.
UNSTABLE EQUILIBRIUM- A body is said to be in a unstable
equilibrium, if it does not return back to its original position and
heels far away when given a small angular displacement.
NEUTRAL EQUILIBRIUM- A body is said to be in a neutral
equilibrium, if it occupies a new position and remains at rest in
this new position when given a small angular displacement.
b
M
W
d
x
G
Fluid
B
R
W
Fluid
M
G
B
x
R
STABLE EQUILIBRIUM (p.66)
M above G
GM ≥ 0
M
W
Fluid
G
B
x
R
Stability of a floating body is determined from the position of
Metacentre (M)
UNSTABLE EQUILIBRIUM (p.66)
M below G
GM ≤ 0
W
G
M
Fluid
B
x
R
NEUTRAL EQUILIBRIUM
GM  0
BM  BG
EXERCISE:
Meyer. Page 75. No.: 4.5 – 4.8.
Douglas Part 1. Page 69. No.: 14, 19.
Determine the submerged depth of a cube of steel 0.4m on each side
floating in mercury. The specific gravities of steel and mercury are 7.8 and
13.6, respectively.
A block of wood of specific gravity 0.7 floats in water. Determine the
metacentric height of the block if its size is 2m x 1m x 0.8m.
A solid cylinder of diameter 4m has a height of 4m. Find the
metacentric height of the cylinder if the specific gravity of the material
of cylinder is 0.6 and it is floating in water with its axis vertical. State
whether the equilibrium is stable or unstable
A solid cylinder of 3m diameter has a height of 3m. It is made up of a
material whose specific gravity is 0.8 and is floating in water with its
axis vertical. Find its metacentric height and state whether its
equilibrium
A cube of 2m side floats in water with half its volume immersed and
the bottom face horizontal. The weight of 340N is moved on the
middle point of one of the top edges of the cube. Determine the angle
through which the cube will tilt under the action of weight, if the center
of gravity of the cube is 0.7m below the geometric center, in a vertical
line through it.
EXPERIMENTAL METHOD OF DETERMINATION OF META CEMTRIC
Under equilibrium, the moment caused by the movement of the load
w through distance x must be equal to the moment caused by the
shift of the center of gravity
A cube of 2 m side floats in water with half its volume immersed and the
bottom face horizontal. The weight of 340 N is moved on the middle
point of one of the top edges of the cube. Determine the angle through
which the cube will tilt under the action of weight, if the centre of gravity
of the cube is 0.7 m below the geometric centre, in a vertical line
through it.