Physics Form One Notes – Pressure
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Concept of Pressure
The Concept of Pressure
Explain the concept of pressure
Pressure is defined as the force per unit area. OR Pressure is the force acting normally
(perpendicularly) per unit surface area
It is calculated by the formula:
Pressure = Force (f)/Area (A)
P=F/A
Where
© P-Pressure
+ F-Force
+ A~Area
The S.1 Unit of Pressure
State the S.1 unit of pressure
‘The SI unit of Pressure is Newton per square metre (N/M’). This unit is usually referred to as the
Pascal (Pa),
1Pa=1 N/M?
‘The other units of pressure are atmosphere, torr bar and mmHg
+ Latmosphere = 780mmHg
. | atmosphere = 1 10° N/M? = Ibar (used by meteorologists)
Note: for a given amount of force, the smaller the area of application the greater the pressure
exerted.
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When a man lifts a bucket of water by its handle that is made with a thin metal, he would
experience some discomfort but if the bucket was made with a thicker handle the discomfort will
be much less if any.
‘This is because the area over which the force is applied is larger.
Pressure due to Solids
Dependence of Pressure on Surface of Contact
Explain dependence of pressure on surface of contact
‘The pressure in solid depends on the surface area of contact. A force (F) applied onto a small
area exerts a higher pressure as compared to when it is applied onto a large surface.
Pressure in solid = Force applied/Area of contact.
Example 1
A block of wood that weighs 30N and measures Sm by 10m by 4m. If it was placed on a table
with the largest possible area (5mx10m) in contact with table, exerts less pressure than it would
when placed with its smallest possible area (5mx4m) in contact with table
Solution
Data:
Force = 30N
Largest base area =?
Av = 10mx5m = 50m*
P= F/A=30N =0.6N/30m”
Pressure = 0.6N/m*
Force (F) = 30N.
Small base are =?
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As=Smx4m
As = 20m?
P= F/A = 30N/20M’ = 1.5 N/M*
Pressure = 1.5 N/M>
Example 2
A tip of needle has a cross- sectional area of 1×10°m’. If doctor applies a force of 2N to a syringe
that is connected to the needle, what is pressure is exerted at the tip of the needle?
Soln:
Data:
Area (A) = 1×10°m?
Force (F) = 20N
Pressure =?
P=F/A
P= 20=2.0×107 N/M”
‘The pressure extended by the needle lip is 2.0×10°N/m*
Example 3
A rectangle metal block with sides 105m by 1.0m by 1.2m rests on a horizontal surface. If the
density of the metal is 7000kg/m3. Calculate the maximum and minimum pressure that the block
can exerts on the surface.
(Take the weight of Ikg mass to be 10N)
Solution:
Data:
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Dimension = 1.2m,1.5m,1.0m.
Density = 7000kg/m*
Maximum pressure (Pmx) = ?
Minimum pressure (Pmn) =?
Volume = 1.2×1.5×1=18m’
Density = mass/ Volume
7000kg/m* = mass/18
Mass = 7000×18 = 126000Kg
Ikg = 10N
126000Kg =?
F = 1260000 = 1.26 x 10°
Force of metal = 1.26 x 10°
Ay = 1.2.x 1.5= 18m?
Ax 1.2m?= 1.2mxim=1.2m?
As= 15x Im= 15m?
Anu = 18m?
Ain = 102m?
Paay = F/Agyy =1.26 x 10°N/18M?= 1.26X10°/1.8 X10!
Maximum pressure = 1.05×10°N/m’/maximum pressure= 0.7×10°N/m*
The Applications of Pressure due to Solids
Identify the applications of pressure due to solids
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It is used to make different objects like screw, nails, pins, spears and arrows. This item is given
sharp points to increase their penetrating power.
It helps some of living organisms for self-defence. A fish uses its sharp fins to protect itself.
When one walks on shoes with sharp pointed heels they exert greater pressure on the ground than
when wearing flat shoes.
It helps in construction of railways. During the constructions of railways, wide wooden or
concrete sleepers are placed below the railways tracks. This provides a larger surface area over
which the weight of the train acts. This is a safety measure to train tracks.
Buildings are constructed with wide foundations to ensure that the weight of the building acts
cover the layer area.
Pressure in Liquids
A liquid will exert pressure on an immersed object as well as on the walls of the container
holding it. Note that the pressure exerted by liquids is due to the weight of the liquid. Also
increase in water level in liquid cause increase in pressure.
The Characteristics of Pressure in Liquids
Describe the characteristics of pressure in liquids
Note: Pressure in liquids =Force/Area
But force= hApg/A
=Hsg
Hence pressure in liquids is given as hsg
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PRESSURE IN LIQUIDS.
| el
H= Height of the liquid column
‘A= Area of the base
The pressure at any point in a liquid at rest then depends
1. Depth
2. Density of liquid
Note: It does not defend on the area
Pressure in liquids is characterized using the following parameters
1. Pressure in a liquid increase with depth
2. Pressure in a liquid acts equally in all directors
3. Pressure in a liquid increases with increase in density of the liquid
Mercury exerts more pressure than an equal volume of water. This because mercury is denser
than water.
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The Variation of Pressure with Depth in Liquids
Examine the variation of pressure with depth in liquids
Demonstration of water spurting from holes at different heights.
VARIATION OF PRESSURE WITH DPETH
As pressure at point A is low due to small height of water above it but at point B the height
increase and the distance of water increase while at point C the height is greatest therefore the
level of water distance will be large distance.
Demonstration of pressure in a communicating vessel
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DEMONSTRATION OF PRESSURE IN A COMMUNICATING VESSEL
x y x 7
H = H . H : H –
‘The shape of vessel found in point A, B, C and D is different but the pressure is the same due to
the equal height (L) of the liquid above the points.
Problems Involving Pressure in Liquids
Solve problems involving Pressure in Liquids
Example 4
A cube of side 2cm is completely submerged in water so that the bottom of the cube is at a depth
of 10cm. use g=10m/s* and s=1000kg/m*
1. What is different between the pressure on the bottom of the cable and the pressure on its
tap?
2. Determine the difference in the force on the top and bottom.
3. What is the weight of the water displaced by the cube?
Solution;
Data.
Depth = 10cm = 0.1m
$= 1000kg/m*
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g= 10m/s
h= Sem= 0.08
formular
p= sgh
p=1000kg/m?x 1 0m/s?x0.1m=1000N/m?
At the h= 0.08m p= 1000x10x0.08= 800N/m
Change in pressure = 1000N/m =200N/m?
So that different in pressure between the bottom the top is 200N/m?
Pressure = Force/Area = P= F/A
Area =L*= (10,02)*= 0.0004m*
Distance in water 200N/m°x0.0004m”
‘This is the upthrust acting on the cube
Water displaced by the cube in weight= volume of the cube
Volume = 13 (2em)?* = Sem?
For water, 1cm*= 1g 50.8cm’ = 8g
Weight of displaced water
mass of displaced water/100=8g = 0.08N
Example 5
Calculate the pressure at the bottom of tank of water 15m deep due to the water above it is
(s=1000kg/m’).
Solution:
Data:
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Height =15m
S=1000kg/m*
g= 10m/s*
Formula
Pressure in liquid sgh
= 1000x10x15=150000N/M?
The Principle of a Hydraulic Pressure
Explain the principle of a hydraulic pressure
It state that “Any external pressure applied to the surface of an enclosed liquid will be
transmitted equally throughout liquid.”
Ilustration of Pascal’s Principle.
THE HYDRAULIC PRESS
” :
oon,
i s
nar,
Note: in all side of vessel will experience equal pressure.
72
‘The hydraulic press works on Pascal’s principle, when using this principle a small force
converted into a large force and vice versa.
From Pascal’s Principle
Py=Pp
E,=E2
Ay A
Fo Fy, ag, but Fy=P,
Ay
Fo=Py,Az
OR
Fo= F1,Ag
Ay
Note: The distance moved (d) is inversely proportional to the cross sectional area.
Therefore, d; =A;
dy Ag
therefore dp = A,d,
Example 6
‘The pistons of a hydraulic press have their areas given as 3.””!“TM and 2×10°m? respectively. If
the smaller piston is pushed down with a force of 12N, what is the force required to push the
larger piston?
Soin
Data:
F, = 120N, Ax= 2X10°m*
73
A2=3X10’m?
Therefore, P1=F)=120N = 120 = — 4X10°N/m?
A; 3.0X10~ 3×0.0003
Force on the larger piston
Fp = PoxAg
= 4.0×10°N/M2x 2.0x102m = 8.0x4x10°N
Application of Hydraulic Press
Measure pressure of a liquid
Hydraulic press is used in industries to express bulk items.
APPLICATION OF THE HYDRAULIC PRESS
commoresianchaner a.
Bale of cotine a
4 | I
Pot, eh ton ped wp
Hydraulic brake system
When pressure is applied to the brake pedal, it pushes the piston in the master cylinder forward
creating a pressure in the brake fluid. This pressure is transferred to the slave cylinders where it
or
is multiplied and pushes the brake shoes against the brake dram that is attached to the wheel of
the vehicle.
THE HYDRAULIC BRAKE SYSTEM
rare
re pa
sane
om brake drum
It is used in industries in the forming of metals.
Since the hydraulic press act like a lift, it is used for lifting heavy loads.
Measuring the pressure of liquids using a manometer. Manometer is the device for measuring
pressure (commonly gas).
Atmospheric Pressure
The Existence of Atmospheric Pressure
Describe the existence of atmospheric pressure
Atmospheric pressure is as a result of the weight of this layer of gases, the act at atmospheric
pressure is surrounded the layer of air consisting of a mixture of gases.
Note. The atmospheric pressure on the earth’s surface and objects on the earth is a approximately
1.01×10°N/mTM
75
‘The experiment which demonstrate the existence of atmospheric pressure.
Umbler experiment
TUMBLER EXPERIMENT
ical
When you fill a glass timber with cord and gentle turned upside down, It will be seen that water
will not poured down.
Plunger
76
PLUNGER
Pulling the plunger is not easy. This is so because all the air is squeezed out from the table when
the surrounding pressure being high the plunger sticks.
Crushed bottle
CRUSHED CONTAINER
7
When putting hot water in, the bottle is cooled under cold water the steam condenses; leaving
partial vacuum inside the bottle consequently the greater atmospheric pressure outside the bottle
crushes it in wards.
Applications of Atmospheric Pressure
Identify the applications of atmospheric pressure
A siphon
SIPHON
Ot
A siphon is applied in areas and devices that we use everyday
1. It is used in the toilet flushing cisterns (chain and ball tank). The flush is triggered by a
handle that operates a simple diaphragm like piston pump that lifts enough water.
2. Its used in special rain gauges called siphon rain gauge which are able to automatically
drain out excess water.
3. A siphon cup is a reservoir attached to a gum.
4. Its used is some drainage systems to drain water to one point.
The lift pump
78
LIFT PUMP
‘A lift pump is used to raise water from underground sources. This is a pump that is used to lift
the liquid, rather than force liquid up.
‘A syringe is a simple piston pump that lifts a tube. The plunger that lifts can be pulled and
pushed through inside a cylindrical tube or barrel. This enables the syringe to take in or expel
fluid through the opening (nozzle) at the end of the tube.
SYRINGE
_—
_ [guy
Uses of syringe’
79
1. They can be fitted with hypodermic needles and used to administer injections.
2. They are used to measure liquids and gases in a laboratory.
3. They are used to apply certain compounds such as a glue or lubricant.
Bicycle pump
This is a type of force pump that consists of a hollow metal cylinder and a movable piston.
HAND PUMP
Meassuring Atmospheric Pressure
Measure atmospheric pressure
Atmospheric pressure is measured by using barometer;
‘Types of barometer:
1. The simple barometer
2 Fortin barometer
3. Aneroid barometer
This is a type of force pump that consists of a hollow metal cylinder and a movable piston
80
A simple barometer is the most fundamental of the other types of barometer. The barometric
liquid used is mercury.
A simple barometer consists of a hard glass tube closed at one end.
‘SIMPLE BAROMETER
oe
i (orien ernn arenes
Ht
Fortin barometer
A Fortin barometer is a modified simple barometer. It consists of an inverted tube closed at its
upper end with the lower open end immersed in a reserve of mercury. The atmospheric pressure
is measured in terms of the height of the column of mercury
FORTIN BAROMETER
.
81
Disadvantages of Fortin barometer:
1. Mercury is very expensive to use and is very toxic. For these reasons, an aneroid
barometer is usually preferred.
2 It is not portable as it is generally big and contains liquid.
3. It must be mounted in a vertical position
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