Download - 8 week Lectures
Liquids and Gases
Pressure, Pascal’s principle
How do they lift your car for service?
Atmospheric pressure
We’re submerged!
How can you drink a Coke?
Archimedes ! Eureka!!!
Balloons of all sizes
Bubbles of all sizes
3/1/2017 Physics 214 Spring 2017 1
8th week Lectures Feb. 27. – March 03. 2017.
3/1/2017 Physics 214 Spring 2017 2
Liquids and Gases
As we know liquids and gases act very differently than solids.
Liquids and gases have mass but their constituent atoms are not bound so that each part of the liquid or gas can move.
The atoms of a liquid are more tightly bound so a liquid can be kept in an open container whereas gas usually requires a closed container.
Liquids, like solids are not very compressible, that is, it is difficult to change the volume.
A volume of gas can have it’s volume changed fairly easily. Both have the property of being able to flow, for example water and gas lines in a house.
The unit of volume is
the meter cubed , m3,
which is a very large
volume. Very often we use
cm3 = cc. Other everyday
units are gallons, quarts,
pints
3/1/2017 Physics 214 Spring 2017 3
Pressure
A volume of liquid or gas has mass and F = ma is still a good law except a force at a point on the surface of water only moves the water near that point
So generally we work with liquids and gases in containers
and exert forces over a surface.
We define pressure (P) as: P = F/A
that is the force (F) divided by the area (A) over
which the force acts.
Any change in pressure of an enclosed fluid at
rest is transmitted uniformly throughout the liquid.
This is Pascal’s principle.
The dimension of pressure is N/m2 and its unit is 1N/m2 = 1Pascal
3/1/2017 Physics 214 Spring 2017 4
Hydraulic Jack
If the liquid levels in each cylinder
on each side are at the same height
then the pressure F/A just below
each piston is the same and
F1/A1 = F2/A2 so F2 = F1A2/A1
If we make the ratio of the surfaces
A2/A1 = 100 then an F1 force of 50lbs
can generate a lift force .
Of course if we push F1 down a distance h1 then the F2
Side will only rise h1 A1/A2 because h1A1 = h2A2, that is the displaced volumes must be the same.
Work done = F1h1 = F2h2
2F = 5000Lbs
3/1/2017 Physics 214 Spring 2017 5
Atmospheric pressure
If I stack a pile of bricks each brick has to support all
the bricks above it. So as we go down the stack the
force increases as does the pressure. Denote the
mass of a brick by “m” and its surface “A”
In the example shown the gravitational force on the face
of the bottom brick would be and the
pressure
At the earths surface we are supporting
a column of air which exerts a force and
because it is a gas it exerts an equal pressure
In all directions.
g
6F mg
6F mg
6mgP
A
3/1/2017 Physics 214 Spring 2017 6
2A-01 Suction Cups
How does a
suction cup
work ?
Remember atmospheric pressure can support 32 feet of water so the force on 1 square foot is ~ 2000 lbs!
How does a suction cup ‘hold on’ to objects?
Holding the suction cup by
itself I only have to support the
weight since the force due to
atmospheric pressure acts on
the top and bottom of the cup.
If I place it on a surface and
exclude all the air the cup is
held to the surface by a force
due to atmospheric pressure
of 1.013x105 Pascals per
square meter F = PAA
PA
F F
If two cups are
pushed together,
does this make
it twice as
difficult to
separate ?
PA
3/1/2017 Physics 214 Spring 2017 7
Otto von Guericke 1602 - 1686 was the “inventor” of
the “nothing” we now call a vacuum.
Von Guericke created a
vacuum by attaching two
hemispheres and then
evacuating the air from
the resultant sphere. Von
Guericke demonstrated
the force of the vacuum
before the German
emperor Ferdinand III by
having two teams of
eight horses attempt to
disengage the
hemispheres.
He was the mayor of the German city of Magdeburg. He built the “Hemispheres
of Magdeburg” and constructed the first vacuum pump.
3/1/2017 Physics 214 Spring 2017 8
2D-01 Hydraulic Press
THE INPUT FORCE IS GREATLY ENHANCED BY THE HYDRAULIC FLUID AND BY THE LEVERAGE GAINED USING THE LONG
HANDLE.
Within the Hydraulic fluid the pressure is uniform:
F1/A1 = F2/A2 F1/F2 = A1/A2
Pump piston diameter = 0.5 in
Lift piston diameter = 1.25 in
F1= 6.25*F2
This is not enough mechanical advantage to
crush the wood. How is it done?
Is it possible to
crush a 2x4 only
with the force
exerted by one
hand ?
Remember, the lever arm also gives a mechanical
advantage. We have: F1≈ (16)*6.25*F2 = 100*F2
Using the uniformity of pressure within a
liquid as a mechanical advantage
3/1/2017 Physics 214 Spring 2017 9
2D-03 Pascal's Principle (Wine Bag)
BY CREATING A PRESSURE WITHIN A VESSEL, A PRESSURE IS EXERTED ON ALL THE WALLS OF THE VESSEL. THIS MEANS A
FORCE = PA WHICH IS LARGE ENOUGH TO LIFT A PERSON
Creating a Pressure to exert a Force
Is it possible to
lift a heavy
object using
only your
breath ?
P = F/A F = PA
A pressure applied over an area
can generate a large force.
3/1/2017 Physics 214 Spring 2017 10
2A-05 Pressure Force Milk Jug
Liquid takes up a much smaller volume than steam. As the
steam cools and condenses a partial vacuum forms and the
pressure drops. Atmospheric pressure then crushes it.
Effect of atmospheric pressure on a partially evacuated milk bottle
The hot liquid heats the air
which expands and some
leaves the container. The
hot liquid also causes
vapor to form in the jug
which then cools and
condenses.
What will happen
to the container
if it is sealed
after putting in a
small amount of
very hot water?
3/1/2017 Physics 214 Spring 2017 11
Density
If one takes two objects of exactly the same volume made of
different materials they have different weights. So we define
a useful quantity called density and denoted by .
Density ρ = mass/unit volume, kg/m3 or grams/cc so the
mass of an object is ρV and the weight ρVg
If an object is put into a container of liquid
it will float if ρobject is less than ρliquid
It will sink if ρobject is greater than ρliquid
3/1/2017 Physics 214 Spring 2017 12
Density and pressure
If I take a container of liquid the pressure at any depth is the weight of the water above that depth divided by the area.
It is very useful to define
Mass/unit volume ρ = kg/m3.
Very often we use grams/cubic centimeter
1 gram/cm3 = 1000kg/m3
Water is 1 gram/cc
W = mg = ρAhg
Pressure P = W/A = ρgh and the pressure is the same at all depths increasing with depth. This is the pressure increase from the surface
which is also subject to atmospheric pressure
g
3/1/2017 Physics 214 Spring 2017 13
Can you guess what happens when
Shaving Cream is placed in vacuum ?
Do the balloons
burst in vacuum
differently then they
normally burst ?
2A-03 Vacuum Demos
Effects of Vacuum on objects made largely of air or air pockets.
Why do the
balloons burst
in the vacuum ?
What will happen when
the marshmallows are
returned to normal
pressure ?
Why do the
marshmallows
get bigger in
vacuum ?
AN AIR-POCKET/BALLOON WILL EXPAND WHEN THE PRESSURE IS REDUCED AND IT WILL DEFLATE WHEN THE PRESSURE IS INCREASED. SO BALLOONS WILL EXPAND AS THEY RISE IN THE ATMOSHPERE AND THE EXPANSION OF A PARTIALLY EVACUATED CAN IS USED IN BAROMETERS.
3/1/2017 Physics 214 Spring 2017 14
2B-04 Liquid Pressure
AT ANY GIVEN POINT IN A STATIONARY LIQUID, THE PRESSURE IS THE SAME IN ALL DIRECTIONS.
PRESSURE IS NOT A VECTOR. IT ACTS
EQUALLY IN ALL DIRECTIONS
Investigating Pressure in different directions within a liquid in equilibrium.
IF A LIQUID IS IN EQUILIBRIUM, THE
FORCES ACTING AT A POINT CANNOT
HAVE A PREFERENTIAL DIRECTION OR
THE LIQUID WOULD MOVE.
The increase in pressure ρgh is
measured by the difference in
height of the liquid in the U tube.
A B B A
h g
What will happen
to the reading on
the manometer as
the sensor is
rotated ?
3/1/2017 Physics 214 Spring 2017 15
2B-05 Pressure Forces in Liquids
THE LIQUID PRESSURE DEPENDS ONLY ON DEPTH P = ρgh.
THE UPWARD FORCE DEPENDS ON THE AREA F = PA
What happens as
the submerged
cylinder filled
with air is filled
with water ?
Air
Water
An open ended cylinder kept shut by liquid pressure
There are two forces acting
on the plate. It’s weight
down and PA up. When PA
exceeds the weight the
cylinder stays intact
In this situation the plate
has to now support the
weight of the water and
when the weight of the
water plus plate exceeds PA
the cylinder opens
PA
PA
3/1/2017 Physics 214 Spring 2017 16
If the different
vessels were filled
to the same height,
how does the
pressure differ at
each vessel base ?
2B-02 Pascal's Vases
THE PRESSURE IS DEPENDENT ONLY ON THE HEIGHT h AND NOT THE VOLUME OR SHAPE OF THE VESSEL.
P = ρgh
Examining the Pressure at the bottom of
differently shaped vessels filled with fluid
3/1/2017 Physics 214 Spring 2017 17
2B-03 Water Seeks Own Level
LIQUID PRESSURE DEPENDS ONLY ON VERTICAL HEIGHT (MEASURED STRAIGHT DOWN THAT IS PARALLEL TO g).
P = ρgh
The slanted cylinder
and twisted cylinder
hold a longer “total
length” of water. But in
each case the vertical
height is the same.
Liquid pressure
depends on the
“height” of the
liquid column.
But how is this
height measured ?
Investigating the Dependence of Pressure on Height
3/1/2017 Physics 214 Spring 2017 18
In our everyday lives we do not feel we are supporting a very large weight because it is the environment in which we have developed.
Galileo’s disciple Torricelli invented the Barometer. He used a meter long glass tube, sealed one end and left open the other.
He filled the tube with mercury and hold his finger over the open end. Inverted the tube and placed the open end into a container of mercury. So that all the air bubbles were removed he raised the tube to a vertical position.
Some of the mercury flowed from the glass tube into the mercury container until an equilibrium was reached. A 760mm high column of mercury was supported by the atmospheric pressure.
No Air
Vacuum
g
P is the same
Determination of Atmospheric Pressure
Using a Barometer
3/1/2017 Physics 214 Spring 2017 19
Knowing the density of mercury and the height h of the column of mercury
We can calculate the mass of a 0.76m high and base cube of mercury
313600 /
0.76
mercury kg m
h m
21m
2 3 2
2
2 2 2 2 5
2 2
2 2
2 5 2
/ 13600 / 0.76 10336 /
Next we calculate the weigh/m = pressure
Weight/m / 10336 / 9.8 / 1.013 10
Since / and thus / (See page 4)
/ 1.1013 10 / 1.
Mass m kg m m kg m
mkgF m kg m m s
s m
mkg s Newton F m Pascal
F m p N m
5
5
1013 10 ( )
1Atmosphere 1.013 10
1Atmospere 14.696 / in
This is equal to for the Mercury
Pa Pascal
Pa
pounds sq
gh
3/1/2017 Physics 214 Spring 2017 20
Everyday examples
Suction cups – remove the air and the atmosphere holds it in place.
Drinking through a straw – create a partial vacuum in your mouth and the atmospheric pressure pushes the fluid up the straw
Pressure is lower at higher altitudes – water boils at a lower temperature
Pressure is higher the deeper you go in the ocean – leads to more nitrogen being absorbed and the bends.
3/1/2017 Physics 214 Spring 2017 21
Suction cup
Question: What is the minimum area of a
suction cup that can be used to lift 100kg.
The suction cup will stay attached to the block
providing PA is greater than F/A. In practice
there would only be a partial vacuum under the
cup so the cup would break away from the
block at a lower force and pressure.
1.013 x 105 x A = 100 x 9.8 A = 9.67/1000m2
Which would be a circle of radius just over 2
inches
mg
F PA
3/1/2017 Physics 214 Spring 2017 22
Archimedes Principle If an object is lowered into a liquid
the volume it occupies was being supported by an
upward force that exactly balanced the weight of
the same volume of liquid so the object will feel the
same upward buoyant force.
buoyant force = weight of liquid displaced
this is true for objects that are immersed and for
objects that float. So a boat made of steel can float
because it can displace a volume of liquid greater
than it’s own weight. A large volume of the boat is
air so the average density is less than that of water.
T + FB = W = mg
g
T
mg
Fb
3/1/2017 Physics 214 Spring 2017 23
Floating and buoyant force If a floating object is submerged to a depth h then the pressure on the bottom is ρgh and the upward force is ρghA but hA is the volume of liquid displaced, V, and ρgV is the weight of liquid displaced so the
Fb = weight of liquid displaced = weight of object
ρliquid x Vdisplaced x g = ρobject x Vobject x g
If an object has a density larger than the liquid it will sink. Suppose the top is at a depth of dt and the bottom at db. Then there is downward pressure on the top ρgdt and an upward pressure on the bottom ρgdb so the net buoyant force
Fb = ρg(db – dt)A
= ρgV = weight of liquid displaced.
T + Fb = weight of the object = mg
g
Fb
g
Fb
T
3/1/2017 Physics 214 Spring 2017 24
Which object
experiences the
greater buoyant
force, the
heavier one or
lighter one ?
2B-08 Buoyant Force
BUOYANT FORCE DOES NOT DEPEND ON THE MATERIAL OF
THE OBJECT DISPLACING THE FLUID. THE BUOYANT FORCE
DEPENDS ONLY ON THE VOLUME OF FLUID DISPLACED.
T
Mg
T
Mg
FB
Scale reads
tension in cord:
T = Mg – FB
Mg = FB + T
We find Fb to be exactly equal
for both masses
Compare the Buoyant Force between two
cylinders of equal volume and different mass.
3/1/2017 Physics 214 Spring 2017 25
What happens to
the reading on
the upper scale
when the block is
lowered into the
beaker of water ?
2B-09 Archimedes I
EVEN THOUGH THE BLOCK DOES NOT ‘TOUCH’ THE LOWER SCALE, THE FORCE ON THE
FLUID DUE TO THE BLOCK IS TRANSMITTED TO THE SCALE. THE REDUCTION IN READING ON
THE UPPER SCALE IS EXACTLY EQUAL TO THE INCREASE IN READING ON THE LOWER SCALE.
IF THE CONTAINER WAS FULL SO THAT WHEN THE BLOCK WAS INSERTED THE VOLUME THE
BLOCK DISPLACED SPILLS OUT OF THE CONTAINER THEN THE BOTTOM SCALE WOULD NOT
CHANGE.
The fluid exerts a
buoyant force on the
block, which reduces
the tension on the
cord. The reading on
the scale is lowered.
T
Mg
FB
T = Mg – FB
Should
anything
happen to the
reading on the
lower scale ?
Since the fluid exerts a force on the
block, the block exerts an EQUAL
and OPPOSITE force on the fluid.
3/1/2017 Physics 214 Spring 2017 26
2B-10 Archimedes II
A. The block is not immersed T1 = Mg
B. The block is immersed but the liquid runs out T2 = Mg – FB
C. The displaced liquid is poured into the can T3 = Mg – FB + WDF
T1 is found to equal T3 which means that the bouyant force FB is
equal to WDF the Weight of the displaced Fluid
THE BUOYANT FORCE IS EQUAL TO THE WEIGHT OF THE FLUID DISPLACED.
Use a scale to establish the relationship between the Buoyant
Force on an object and the Weight of Fluid Displaced by the object
T1
Mg
A
T2
Mg
FB
B
T3
Mg
FB
WDF
C
3/1/2017 Physics 214 Spring 2017 27
Does the air
exert a buoyant
force ?
2A-08 Buoyancy of Air
IF SENSITIVE WEIGHING OF AN OBJECT IS REQUIRED,
UNEQUAL BUOYANT FORCES COULD AFFECT THE RESULTS.
mbg
mag
ρairgVb ρairgVa
Setting the sum of torques on equal-arm balance
about pivot equal to zero, we have in the presence
of air:
mag – ρairgVa = mbg - ρairgVb
Vb > Va implies mb > ma which is demonstrated in
vacuum
Investigating the Buoyant force resulting from Air
3/1/2017 Physics 214 Spring 2017 28
Pressure and Volume of a Gas
In the apparatus shown the pressure at
point A is the same as at point B so the
pressure exerted by the gas is equal to
ρgh.
If we add more mercury we can
measure both pressure and volume
and if the temperature does not change
we find
PV = constant
A B
B A
h
g
3/1/2017 Physics 214 Spring 2017 29
Summary of Chapter 9
P = F/A Pascals
F1/A1 = F2/A2
Work done = F1h1 = F2h2
1 Atmosphere = 1.013 105 Pa
and will support
76cm of mercury
32 feet of water
No Air
g
3/1/2017 Physics 214 Spring 2017 30
Liquids
P = W/A = ρgh
Water is 1 gram/cc
1 gram/cm3 = 1000kg/m3
buoyant force = the weight of liquid displaced
T + FB = W = mg
For a floating object T = 0
g
T
mg
Fb
3/1/2017 Physics 214 Spring 2017 31
Balloons
Any object in the atmosphere is subject
to a buoyant force and Archimedes law
applies so if the buoyant force is greater
than the weight of an object it will rise.
So since the material of a balloon has a
density greater than air then the balloon
must be filled with a gas having a
density less than air. In practice balloons
either use Helium or hot air.
As the balloon rises the buoyant force
decreases because the density of the air
decreases and the balloon will float at
constant altitude when the buoyant force
is equal to the weight.
mg
FB
3/1/2017 Physics 214 Spring 2017 32
Surface tension
The molecules and atoms in a liquid are
continually in motion so that a molecule at
the surface can escape and this is
evaporation. However a molecule at the
surface feels an attractive force pulling it
back into the liquid and this is surface
tension. This is the reason that one can
form bubbles and water drops
3/1/2017 Physics 214 Spring 2017 33
Questions Chapter 9
Q1 Is it possible for a 100-lb woman to exert a greater pressure on
the ground than a 250-lb man? Explain.
Q3 The same force is applied to two cylinders that contain air.
One has a piston with a large area, and the other has a piston with
a small area. In which cylinder will the pressure be greater?
Yes. The pressure will be mg/A so if A is small e.g. small
heels the pressure will be very large
The pressure is F/A so the one with the smallest A
3/1/2017 Physics 214 Spring 2017 34
Q4 A penny and a quarter are embedded in the concrete bottom of
a swimming pool filled with water. Which of these coins
experiences the greater downward force due to water pressure
acting on it?
Q5 Why are bicycle tires often inflated to a higher pressure
than automobile tires, even though the automobile tires must
support a much larger weight?
Each coin has to support the weight of water in a vertical column
so the quarter has the biggest force F =PA
Once again the upward force has to support the weight so
F = mg but F = PA where A is the area of the tire on the road so
M/m = (PA)car/(Pa)bike so Ma/mA = Pcar /Pbike the ratio of the areas is
smaller than the ratio of the weights so
Pbike is higher.
3/1/2017 Physics 214 Spring 2017 35
Q6 The fluid in a hydraulic system pushes against two pistons, one
with a large area and the other with a small area.
A. Which piston experiences the greater force due to fluid pressure
acting on it?
B. When the smaller piston moves, does the larger piston move
through the same distance, a greater distance, or a smaller distance
than the smaller piston?
Q8 When a mercury barometer is used to measure atmospheric
pressure, does the closed end of the tube above the mercury
column usually contain air?
A. The pressure is the same and F = PA so the larger piston has
the larger force.
B. The work done is the same so the small piston moves the most
No it needs to be a vacuum
3/1/2017 Physics 214 Spring 2017 36
Q9 Could we use water instead of mercury to make a barometer?
What advantages and disadvantages would be associated with the
use of water?
Q10 If you climbed a mountain carrying a mercury barometer,
would the level of the mercury column in the glass tube of the
barometer increase or decrease (compared to the mercury
reservoir) as you climb the mountain?
The height of the liquid depends on the density. So one can use
water but the column would be 32 feet high
The pressure decreases because you have a smaller column of
air to support so the height would decrease
3/1/2017 Physics 214 Spring 2017 37
Q11 If you filled an airtight balloon at the top of a mountain,
would the balloon expand or contract as you descend the
mountain?
Q12 When you go over a mountain pass in an automobile,
your ears often “pop” both on the way up and on the way
down. How can you explain this effect?
It would contract because the atmospheric pressure would
increase and the pressure inside the balloon would increase to
balance this change
As you go up or down the atmospheric pressure changes and the
popping is the inner ear adjusting to the pressure change
3/1/2017 Physics 214 Spring 2017 38
Q15 Is it possible for a solid metal ball to float in mercury?
Q16 A rectangular metal block is suspended by a string in a
breaker of water so that the block is completely surrounded by
water. Is the water pressure at the bottom of the block equal to,
greater than, or less than the water pressure at the top of the
block?
The upward force is the weight of liquid displaced and the
downward force is the weight of the ball. If the density of the
liquid is greater than that of the ball it will float.
The pressure is ρgh so the pressure is higher at the bottom. The
difference in pressure provides the upward force on the block
3/1/2017 Physics 214 Spring 2017 39
Q19 A large bird lands on a rowboat that is floating in a swimming
pool. Will the water level in the pool increase, decrease, or remain
the same when the bird lands on the boat?
Q20 A rowboat is floating in a swimming pool when the anchor
is dropped over the side. When the anchor is dropped, will the
water level in the swimming pool increase, decrease, or remain
the same?
The buoyant force is the weight of liquid displaced so to
support a larger weight more liquid is displaced and the level
rises
When the anchor is in the boat it’s whole weight is supported and the
amount of water displaced balances that weight. When it is thrown
overboard it sinks and only displaces it’s volume so the water level
falls
3/1/2017 Physics 214 Spring 2017 40
Q22 If an object has the same density as water, will the object float
to the top, sink to the bottom, or take neither course?
Providing the object and water are incompressible the object
will stay at whatever depth it is placed. It will not sink or rise.
3/1/2017 Physics 214 Spring 2017 41
Ch 9 E 4
Pressure of gas in piston = 300 N/m2.
Area of Piston = 0.2m2.
What is force exerted by piston on gas?
P = F/A, F = PA = 300 N/m2 (0.2 m2) = 60 N
A = 0.2m2
p = 300 N/m2
3/1/2017 Physics 214 Spring 2017 42
Ch 9 E 6
Hydraulic system: A2 = 50 A1
F2 = 6000 N. What is F1?
Pressure is the same just underneath each piston
F1/A1 = F2/A2
F2/F1 = A2/A1 = 50A1/A1 = 50
F1 = F2/50 = 6000/50 = 120N
A1 A2
F2 = 6000N.
3/1/2017 Physics 214 Spring 2017 43
Ch 9 E 8 T = constant, P1 = 10 kPa, V1 = 0.6 m3.
P2 = 90 kPa, V2 = ?
P1V1 = P2V2
(10 kPa)(0.6 m3)/(90 kPa) = V2 = 1/15 = 0.067 m3
P1 = 10 kPa
V1 = 0.6 m3 P2 = 90 kPa
V2 = ?
3/1/2017 Physics 214 Spring 2017 44
Ch 9 E 12
Boat displaces 2.5 m3 of water.
Density of water H2O = 1000 kg/m3.
a) What is the mass of water displaced?
b) What is the buoyant force?
a) Mass of fluid displaced
(mFD) = volume x density of fluid.
MFD = VFDH2O = (2.5 m3)(1000 kg/m3) = 2500 kg
b) Buoyant force equals weight of fluid displaced.
Fb = WFD = mFD g = (2500 kg)(9.8 m/s2) = 24500 N
Fb = WFD
3/1/2017 Physics 214 Spring 2017 45
Ch 9 E 14
Stream moves at v1 = 0.5 m/s in cross sectional area A1.
Stream reaches point where A2 = ¼ A1.
What is v2?
a) v1A1 = v2A2
(0.5 m/s)(A1) = v2(¼A1)
v2 = 2 m/s
V1 V2
A1 A2
3/1/2017 Physics 214 Spring 2017 46
Ch 9 E 16
Wing has a cross sectional area A = 10 m2. Wing
experiences Lift = 60000 N.
What is the difference in air pressure b/w top and
bottom of wing?
a) P = F/A , Pb – PA = F/A = 60000N/10m2 = 6000Pa
A = 10m2
Pb
Pt
60000 N
3/1/2017 Physics 214 Spring 2017 47
Ch 9 CP 2 Water density = H2O = 1000 kg/m3. Depth of swimming pool = 3m.
a) What is the volume of a column of water 3m deep and cross
sectional area 0.5 m2?
b) What is its mass?
c) What is its weight?
d) What is the excess pressure exerted on the pool bottom?
e) Compare to atmospheric pressure.
a) V = Ad = (0.5 m2)(3m) = 1.5 m3
b) M = V = (1.5 m3)(1000 kg/m3) = 1500 kg
c) W = Mg = (1500 kg)(9.8 m/s2) = 14700 N
d) P = F/A = 14700N/0.5m2 = 29400 Pa
e) Atmospheric Pressure is about 100 kPa
P is about 30 kPa
P/Atm = (29400 Pa)/(1.013 x 105 Pa) = 0.29
3m
0.5m2
3/1/2017 Physics 214 Spring 2017 48
Ch 9 CP 4 Wooden boat: 3m x 1.5m x 1m that carries five people.
Total mass of boat and people equals 1200 kg.
a) What is total weight?
b) What is buoyant force required to float?
c) What volume of water must be displaced to float?
d) How much of the boat underwater?
a) W = Mg = 1200 kg (9.8 m/s2)
W = 11760 N
W Fb
3m
1m
b) Fnet = Fb – W = 0
Fb = 11760 N
c) Fb = H2O Vg (see Ch 9 E 12)
Fb/H2Og = 11760N/(1000 kg/m3)(9.8 m/s2) = V = 1.2 m3
d) V = LWh = (3m)(1.5m)h = 1.2 m3 h = 0.27 m