Pressure
The perpendicular force acting per unit surface area is
called pressure.
Pressure(P) = Force(F)/Area(A)
The SI unit of pressure is N/m^2 or Pascal (Pa).
Prove that P=F/A
Solution,
According to the
definition of pressure,
i) Pressure is directly proportional to the
force applied.
i.e P ∝ F ........... (i) (if the area is taken as a constant
term.)
ii) Pressure is
inversely proportional to the surface area.
i.e P ∝ 1/A .......... (ii) (if
force is taken as a constant-term.)
Now,
By combining equations
(I) and (ii), we get,
P∝ F/A
or P= kF/ A where k is the proportionality constant and its
value is 1 in the unit system.
P= 1F/A
P = F/A proved
Question Answers
Name the factors on which the pressure depends.
Factors on which
pressure depends on are:
i) Force
ii) Surface area
Define one Pascal pressure.
When one Newton force is applied or the unit surface area then the pressure is said to be one Pascal
pressure.
What is thrust? Write down its SI unit.
The force which is acting perpendicular to the surface is
called thrust. The SI unit of thrust is
Newton (N).
Give Reasons
The foundation of a building is made wider than walls, why?
The foundation of a building is made wider than walls because the wall of the building and its roof exert
pressure on the wide-area of the
foundation and this reduces pressure over the earth's surface due to which the building is saved from collapsing.
The wheels of a tractor are made larger and flat, why?
The wheels of a tractor are made larger and flat to
reduce the pressure exerted by the tractor as the pressure is inversely
proportional to the surface area. Flat and large tires prevent from descending
into the muddy land.
Camel can walk easily on sand, Why?
Camel has flat soles feet which exert low pressure due to the
bodyweight of a camel. As pressure is inversely proportional to the surface
area, there is less pressure exerted by a flat-soled foot of a camel. Hence,
Camel can walk easily on sand.
Studs are made on the sole of a football player's boot, why?
Football players must have to run with greater speed and turn very fast. Therefore, studs are made on the sole of a football player's
boot to increase the pressure on the ground which prevents the players from
falling and sliding on the ground.
Liquid Pressure
The force exerted by
the liquid per unit area on the wall of the container
is called liquid pressure.
Liquid pressure (P)= height of
liquid(h) * density of liquid(d) * acceleration due to gravity (g)
Prove that: P = hdg
Let, us consider 'h' to be the height of the liquid (water) in a container, 'd' be the density of the liquid, 'g' be the acceleration due to gravity and 'A' be the cross-section area of the container.
Now,
From the definition of pressure,
Pressure(P) = Force(F) / Area(A) [Force = mass(m)x
acceleration due to gravity(g) ]
=(density(d)x
volume(v)x g)/ Area(A) [i.e. mass(m)= density(d) x volume(v)]
=(dxvxg)/A
= (dxAxhxg)/A
= dhg
=hdg
Question Answers
Name the factors on which liquid pressure depends.
Ans. The factors on
which liquid pressure depends are:
i) Depth of the
liquid from its free
surface(h).
ii) Density of the
liquid (d).
iii) Acceleration due
to gravity acting on the liquid (g).
Write down the properties of liquid pressure.
Ans. Some properties
of liquid pressure are as given below:
i) Liquid pressure is
directly proportional to the depth of the liquid from its free surface.
ii) Liquid finds its own level.
iii) Pressure applied
on an enclosed container liquid transmits equally in all directions.
iv) The pressure of liquid does not depend upon the shape and volume of the container in which it is kept.
v) Liquid pressure depends on its density.
Give Reasons
Walls of dams are made thicker at the bottom, why?
Water exerts greater pressure near or at the bottom of the walls of dams as liquid pressure is directly proportional to the depth. Therefore,
the walls are made thicker at the bottom so, they can hold high liquid pressure
exerted by water and prevent the wall from collapsing.
The bottom of a water vessel is made thicker, why?
Water exerts more pressure at the bottom of the vessel as
liquid pressure increases with an increase in depth. So, the bottom of the water
vessel is made thicker to hold the greater pressure exerted by water at the
bottom of the vessels.
Blood pressure in the human body is greater at the feet than at the brain, why?
The distance between the heart and the feet is greater than the
distance between heart and head. As liquid
pressure is directly proportional to the heart and head. As liquid pressure is
directly proportional to the depth of the liquid, so blood exerts
more pressure at the feet of the
human body than at the head. Hence, blood pressure in the human body is greater at
the feet than at the brain.
Pascal's law
Pascal's law state that, "the pressure is equally transmitted perpendicularly to all sides as pressure is applied at a place on a liquid contained in a closed container".
Different machines based on Pascal's law
Some machines based on Pascal's law (application of Pascal's
taw) are:
a. Hydraulic lift
b. Hydraulic press
c. Hydraulic brake
d. Hydraulic crane
Hydraulic lift
The machine based on
Pascal's law which is used to lift the vehicles in automobile servicing stations
during their service is called hydraulic lift.
It is also used to carry people from one floor to another in
tall buildings by multiplying the force.
Hydraulic press or machine
The machine which works on the principle of Pascal's law by converting a little force into a larger force is called a hydraulic machine.
Hydraulic brakes
The machine based on
Pascal's law which is used to stop the heavy moving vehicles like trucks, buses, aeroplanes etc. by applying a little force is called hydraulic brakes.
How can you prove that a hydraulic machine is a force multiplier?
Solution,
The hydraulic machine
consists of two-cylinder tubes of different cross-sectional areas Aland A2 connected together with a horizontal tube.
The apparatus is filled with water The tubes and are provided with the water
and airtight pistons 'A' and 'B' as shown in the diagram. Here, F1be the force applied on the piston
'A' and F2 be the force applied on piston 'B'.
Now,
According to Pascal's law,
Pressure on piston A
(P1) = Pressure on piston B (P2)
or, P1 =P2
or F1/A1= F2/A2 (
when the machine is on frictionless condition)
or, F2 = (F1/A1)* A2
Here F2 is greater than F1 so
it proves that hydraulic machine is a force multiplier.
Density
The density of the substance is defined as the mass of the
substance in per unit volume.
i.e Density = mass/volume
The SI unit of density is kg/m^3 and the CGS unit of density is gm/cm^3.
Relative density
The relative density of a substance is defined as
the ratio of the density of any
substance to the density of water at 4°C.
i.e Relative Density = Density
of substance / Density of water at
Relative density of different substances
|
S.N |
Substances |
Density(kg/m^3) |
Gm/cm^3 |
Relative Density |
|
1 |
Water |
1000 |
1 |
1 |
|
2 |
Milk |
1030 |
1.03 |
1.03 |
|
3 |
Mercury |
13600 |
13.6 |
13.6 |
|
4 |
Ice |
920 |
0.92 |
0.92 |
|
5 |
Gold |
19300 |
19.3 |
19.3 |
What is the density of water at 40°C?
The density of water at 4°C is 1000 kg/m^3 in the SI system of the unit whereas 1gm/cm^3 in the CGS system of the unit.
Upthrust
The resultant upward
force exerted by a fluid on an object which is completely or partially immersed
into the fluid is called upthrust.
Upthrust given by water= Wt. of stone in the air - Wt. of stone in water
Upthrust
(U) =W1- W2
What is the relation of upthrust with the density of the given liquid?
Upthrust is directly proportional
to the density of the liquid. It means
that the liquid with more density applies more upthrust. So, the substance with greater density than
that of water sinks in water whereas
the substance with less density than that of water floats in water.
Archimedes's principle
Archimedes's principle states that "When a body is
wholly or partially immersed in a fluid, it experiences an upthrust which is
equal to the immersed in a fluid,
it experiences an upthrust which is equal to the weight of the liquid displaced by a body."
Experimental verification of Archimedes's principle
Materials required
i)
Eureka can
ii)
Top pan balance
iii)
Stone
iv)
Thread
v)
Spring balance
Procedure
1. Find out the weight of the stone in the air (i.e. W1).
2. Fill the eureka can with water.
3. Keep the beaker over pan balance as shown in the figure.
4. Take the weight of the empty beaker, let it be W2.
5. Immerse the stone wholly into the water of the Eureka can and
note the weight of the stone inside the water. Let it be W3.
6. The water overflows when the stone is immersed into it and
gets collected in the beaker. The weight of the beaker with water is taken. Let
it be W4.
Upthrust (Loss in weight of the stone) W1 - W3.
Weight of displaced water = W4 - W2
Here, it is observed that W1 - W3 = W4 -W2
Thus, loss in weight of a body (upthrust) in liquid is equal
to the weight of the liquid displaced.
Hence, Archimedes's principle is verified experimentally.
Theoretical proof of Archimedes's principle or prove that: U = vdg
To prove that: Upthrust (U) =weight of displaced liquid Solution,
Solution,
Let us consider a body PQRS of Height 'h' and
cross-sectional area 'A' is completely immersed in a liquid of density V. The
height of liquid column above the surface PQ is h1 and above the surface SR is h2.
Here, Pressure on the upper surface of PQ is given by;
P1=h1dgA
Again, Pressure on lower surface of SR is given by
P2=h2dgA
Since, h2 > h1,
Resultant upthrust
(U) = F2- F1
= h2dgA – h1dgA
= dgA (h2 — h1)
= dgAh [i.e. h2-h1= h]
- dgv [ i.e. v = A*h]
- mg [ i.e. m= d*v]
= Weight of displaced liquid.
Hence, Upthrust(U)
=Weight of displaced liquid. proved
Law of floatation
The Law of floatation states that "an object that floats on
liquid displaces the liquid equal to its own weight".
i.e. Weight of
floating object =Weight of displaced liquid
Experimental verification for the law of floatation
Materials required
i. A block of wood
ii. Spring balance
iii. Ureak can
iv. Beaker
v.Top pan balance
Procedure
1. Take the weight of the block of wood. Let it be W1.
2. Fill the Eureka can with water up to the spout and place
the beaker below its spout. Take the weight of the beaker. Let it be W2.
3. Now put the block of wood into the Eureka can. It will
float on water and displace the water.4. The water is collected in the empty
beaker. Let the weight of the beaker with
water be W3.
Weight of displaced water = W3-W2
From the above experiment, it is observed that: W1= W3-W2
i.e. Weight of floating body = weight of the liquid displaced.
Hence, the principle of floatation is verified experimentally.
Conditions for different solids kept in a liquid
1. When the density of a given substance is less than that of a given liquid then, it floats in a liquid.
2. When the density
of a given substance is equal to the given liquid then it remains to suspend at
the same place inside the liquid.
3. When the density
of a given substance is more than that of a given liquid then, it sinks in a liquid.
Some applications of the principle of floatation
a. Hydrometer
b. Ships and boats
C. Icebergs
d. Hot air balloons
Hydrometer
The device which is used to measure the density or relative
density of liquids is called a hydrometer.
When the hydrometer is placed in a liquid, it sinks until it
displaces the liquid equal to its own weight. The hydrometer sinks less in the
liquids having more density and sinks more in the liquids having less density.
Types of hydrometer
There are two types of a hydrometer. They are:
ii. Constant immersion hydrometer.
ii. Constant weight hydrometer.
i. Constant immersion hydrometer
The hydrometer which is to be immersed to the constant level by changing the weight while measuring the density of the liquid is called a constant immersion hydrometer.
It has a constant immersed part in every liquid.
ii. Constant weight hydrometer
The hydrometer whose weight is constant and measure the density of liquid directly is called a constant weight hydrometer.
It has variable immersed parts in different liquids.
Lactometer
A specially designed constant weight hydrometer that is used to measure the purity of milk is called a lactometer.
Atmospheric pressure
The pressure exerted by the mixture of different gases on
the surface of the earth is called atmospheric pressure.
The atmospheric pressure at the sea level is called normal atmospheric pressure or standard atmospheric pressure.
The value of normal atmospheric pressure at sea level is 760
mm of Hg or one atmospheric
pressure is equal to 10^5Pa.
As the amount of air decreases at the height, the
atmospheric pressure also decreases. So, the atmospheric pressure decreases with a decrease in altitude.
Uses of atmospheric pressure
a. It is used to fill ink in the pen.
b. It is used to make syringes.
c. It is used to make an air filling pump.
d. It is used to make tube-well.
Prove experimentally that atmospheric pressure exists.
Method no 1
Take a tin can with a little of the water in it. Take it for a few minutes as shown in figure (a). Close the lid
of the can immediately and cut off the
flame. Now, cool the can under a tap as shown in figure (b). At first, the
pressure of the air inside the can and outside it was equal. When it was heated, the air inside the
can escape out and the space was occupied with the steam. On cooling the can,
the steam condensed creating a partial vacuum inside the can. Hence, the atmospheric pressure is greater outside the can and less inside the tin can due to which the tin can get crushed inward.
This proves that there is atmosphere exerts pressure.
Method no 2
Take a glass filled with water and cover its mouth with cardboard. Invert the glass supporting the cardboard with the help of the palm as
shown in the diagram. Hold the glass in your hand and remove the other hand
slowly which was supporting the cardboard.
The atmosphere exerts pressure upwards on the cardboard due to which the
cardboard and the water do not fall.
This shows that there is atmospheric pressure.
Barometer
The instrument which is used to measure the atmospheric
pressure of a certain place is called a barometer.
There are two types
of barometers. They are:
i. Mercury barometer
ii. Aneroid barometer
Explain the construction and working process of the mercury barometer
Construction
of mercury barometer
A normal mercury barometer consists of one meter long
graduated glass tube, closed at one end, completely filled with mercury and
inverted vertically into the mercury-filled trough.
Working process of the mercury barometer
The gap or vacuum called Torricellian vacuum is created at the tube above the level of mercury inside the tube in a barometer due to the effect of atmospheric pressure. When the atmospheric pressure increases, the mercury level in the glass tube of the barometer rises up and when the atmospheric pressure decreases, the mercury level in the glass tube falls down. The level of mercury in the glass tube shows the atmospheric pressure of a place.
Air filling pump
A simple device which
is used to pump (fill) the air in tubes of tires of bicycles or tubes of
volleyball, football etc. and based on the principle of atmospheric pressure is
called air filling pump.
Explain the construction and working process of the air filling pump.
Construction of the air filling pump
The air filling pump consists of a cylinder, piston and nozzle. The cylinder is connected with a
nozzle at one end and its other end is open. A piston with a rubber or leather washer is put through it. The other end of the piston is connected with a
handle.
Working Process of the air filling pump
To fill the air inside the tubes, the piston must be moved up and down continuously. While pulling the piston up, there creates a vacuum inside the cylinder. In this vacuum air is filled from the atmosphere as we push the piston down, the air enters into the tube through the nozzle of the cylinder. Similarly, when we push the piston up, air from the tube can not come back out as there is a valve in the tube, which get closed automatically. This process is continued to fill the tube completely.
Water pump or tube well or Hand pump
The water pump is an instrument that
is used to pull underground water and based on the principle of atmospheric
pressure.
Explain the construction and working process of Water-pump OR Tube-well OR Hand pump.
Construction of water pump
Numerical Problems From Exercise
Find the pressure exerted on the bottom of the pond having a depth of 1.5m.
Solution,
Given,
Depth of pond(h) =
1.5m
Density of water
(d) = 1000 kg/M^3
Acceleration due to
gravity (g) = 9.8 m/s^2
Pressure (P) = ?
Now,
By using formula,
P = hdg
= 1.5 x 1000
x9.8
= 14700 Pa
= 1.47 x 104Pa
If your mass is 45 kg, what weight of water is to be displaced by you to float in water, why?
Solution,
Mass of a body (m)
= 45kg
Acceleration due to
gravity (g) = 10 m/s^2
Weight of a body
(W) = m x g
= 45 x 10
= 450 N
Here, according to the law of floatation, a floating body
must displace the liquid equal to its
own weight.
Hence, 450 N weight of water must be displaced by my body in
order to float in water.
A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000kg. The area of cross-section of the piston carrying the load is 425 cm^2. What maximum pressure would the smaller piston have to bear?
Solution,
Mass of car (m) = 3000kg
Load on the
piston(F) = m x g
=
3000 x 9.8 N
= 29400 N
Cross-section area
of carrying load (A) = 425 cm2
= 0.0425m2
Now,
Pressure(P) = Force(f) /
Area(A)
=691,764.70 Pa
=6.91x 105Pa.
Therefore, the hydraulic machine is based on Pascal's law so, pressure on the small piston and the large piston is equal which is 6.91 x 105Pa.
Question Answers
What is the difference between the floating of an empty ship and a cargo-loaded ship?
The weight of an empty ship is less than that of the cargo-loaded
ship. So, less part of an empty ship
immerges in water than that of a cargo loaded ship while floating in the water.
What difference is observed if an egg is immersed in pure water and in concentrated salt solution? Write with reason.
If an egg is immersed in pure water, it sinks because the
up-thrust due to pure water is less than the weight of the egg. Similarly, the
egg floats on the concentrated salt solution because the up-thrust due to the concentrated salt solution is more than the weight of the egg.
The bags are provided with broad handles, why?
The bags are provided with broad handles because the
pressure is inversely proportional to
the surface area, so the wide handle of the bag distributes the pressure due weight of the bag over a large area which makes it easier to carry the bags.
It is easier for a man to swim in seawater than in river water. Give reason.
We know that the up-thrust of the liquid is directly
proportional to the density of the liquid. The seawater has more density than
that of river water due to the dissolved salts so that the sea-water exert of
river water due to the dissolved salts so that the sea-water exert more
up-thrust to our body than that of river water and so, it is easier to swim in seawater than in river
water.