Buoyancy

1
Buoyancy Stability of Body
Lecture13
SCS138 Applied Physics
Dr. Bunyarit Uyyanonvara IT Department,
Sirindhorn International Institute of
Technology Thammasat University
2
Sections Overview

• Lecture 11 Fluids, Density Pressure
• Lecture 12 Forces on Plane Curved surfaces
• Lecture 13 Buoyancy Stability of bodies
• Lecture 14 Fluid flow concepts
• Lecture 15 Review Tutorial

3
Pascal s Principle

• A change in the pressure applied to an enclosed
  incompressible fluid is transmitted undiminished
  to every portion of the fluid and to the walls of
  its container.

4
Pascal s Principle

• Consider the case in which the incompressible
  fluid is a liquid contained in a tall cylinder.
• A cylinder is fitted with piston on which a
  container of lead shot rests.

5
Pascal s Principle

• The pressure p at any point P in the liquid is
  then

6
Pascal s Principle

• Lets add more weight to the container to
  increase pext.
• The quantities ?, g and h are all unchanged.
• So the pressure change at P is

7
Pascal s Principle

• The pressure change is independent of h, so it
  must hold for all points within the liquid, as
  Pascals Principle states.

8
Hydraulic Lever

• Let an external force of magnitude Fi directed on
  the left hand (or input) piston
• Whose area is Ai.

9
Hydraulic Lever

• An incompressible liquid in the device then
  transfer the pressure throughout the liquid body.
• Produced an upward force of magnitude Fo on the
  right hand (or output), area Ao.

10
Hydraulic Lever

• The change ?p in the pressure of the liquid is
  given by
• so

11
Hydraulic Lever

• If we move the piston down a distance di, the
  output piston move upward a distance do, then

12
Hydraulic Lever

• In terms of works done by the piston
• With a hydraulic lever, a given force applied
  over a given distance can be transformed to a
  greater force applied over a smaller distance.

13
Conceptual Check Point I

• What force magnitude F will the larger piston
  sustain without moving ?
• If the small piston has a diameter of 3.8 cm and
  the large piston one of 53 cm, what force
  magnitude on the small piston will balance a 20.0
  kN force on the large piston ?

14
Conceptual Check Point II

• Through what distance must the large piston be
  moved to raise the small piston a distance of
  0.85m ?

15
Conceptual Check Point III

• Three hydraulic levers are used to lift same
  loads to same distances. The levels are identical
  on the input side but differ in the area of
  output piston.
• Lever 1 has output area A
• Lever 2 has output area 2A
• Lever 3 has output area 3A
• for the lift, rank the levers according to
• (a) required work at the input side.
• (b) required magnitude of force at the input side
  
• (c) displacement of the piston at the input side,
  greatest first.

16
Buoyant Force

• When a stationary body is completely submerged in
  a fluid,
• Or floating so that it is partially submerged,
• The resultant fluid force acting on the body is
  call Buoyant Force

17
Buoyant Force

• A net upward vertical force results because
  pressure increases with depth.
• Thus the forces due to this pressure are greater
  in magnitude near the bottom.

18
Buoyant Force

• If we vertically add all the forces from water,
• the horizontal components cancel and
• The vertical add to yield the upward buoyant
  force Fb

19
Buoyant Force

• The buoyant force on a body in a fluid has
  magnitude
• Where mf is the mass of the fluid that is
  displaced by the body.

20
Archimedes Principle

• The buoyant force has a magnitude equal to the
  weight of fluid displaced by the body
• and is directed vertically upward
• This result are commonly referred to as
  Archimedes Principle.

21
Floating

• When a body floats in a fluid, the magnitude Fb
  of the buoyant force on the body is equal to the
  magnitude Fg of the graviational force on the
  body.

22
Floating

• When a body floats in a fluid, the magnitude Fg
  of the gravitational force on the body is equal
  to the weight mfg of the fluid that has been
  displaced by the body.

23
3 characteristics of Fb
24
Conceptual Check Point IV

• We fully submerge an irregular 3kg lump of
  material in a certain fluid. The fluid that would
  have been in the space now occupied by the lump
  has a mass of 2kg
• (a) which direction will the lump move when we
  release it ?
• (b) what happen if we fully submerge the lump in
  a less dense fluid ?

25
Conceptual Check Point V

• Four solid objects are floating in corn syrup.
  Rank the objects according to their density,
  greatest first.

26
Conceptual Check Point VI

• A penguin floats first in a fluid of density ?0,
  then the fluid of density 0.95?0, and then the
  fluid of density 1.1?0
• (a) Rank the densities according to the magnitude
  of the buoyant force on the penguin, greatest
  first
• (b) Rank the densities according to the amount of
  fluid displaced by the penguin, greatest first.

27
Apparent Weight in a fluid

• If the weight is measure within a liquid, an
  apparent weight is related to the actual weight
  of a body and the buoyant force on the body by
• Apparent weight actual weight magnitude of
  buoyant force.
• Note Apparent weight 0 if the body is
  floating, astronauts training.

28
Exercise

• What fraction of the volume of an iceberg
  floating in seawater is visible ?.
• A spherical helium-filled balloon has a radius R
  of 12.0 m. The balloon, support cables and basket
  have a mass m of 196 kg. What maximum load M can
  the balloon support while it floats at an
  altitude at which helium density ?He is 0.160
  kg/m3 and the air density ?air is 1.25 kg/m3?
• Assume that the volume of air displaced by the
  load, support cables, and basket is negligible.

29
Exercise

• A metal rod of length 80 cm and mass 1.6 kg has a
  uniform cross-sectional area of 6.0 cm2 . Due to
  the non-uniform density , the center of mass of
  the rod is 20cm from one end of the rod.
• (a) What is the tension of the rope close to the
  center of the mass ?
• (b) What is the tension of the rope farther from
  the center of the mass ?
• (hint the buoyancy force on the rod effectively
  acts at the rods center)

30
Important topics in this lecture

• Pascal Principle
• Hydraulic Lever calculation
• Buoyant force
• Archimedess principle
• Floating
• Apparent weight