PRESSURE
FORMULA
• AREA
- Rectangle = l x w
- Square = s ^2
- Circle = ∏ r ^2
- Cylinder = 2 ∏ r h
- Sphere = 4 ∏ r ^2
• VOLUME
- Cuboid = l x w x h
- Cube = l x l x l
- Cylinder = ∏ r ^2h
- Sphere = 4/3 ∏ r ^3
Examples usage of pressure
• sharp knife- has very small • Skis have a large area to
surface area on its cutting
reduce the pressure on
edge, so have higher
the snow, so they do
pressure
not sink in too far
• nails, needles, pins-sharp
ends, very small surface
area
• spikes on cleats- pressure
on studs high enough for
them to sink in ground to
give extra grip
• tractor moving on soft
ground has wide tires to
reduce pressure on the
ground to avoid sinking
500N
The block in the following diagram has a weight of 1200
N. The block is turned so that it rests on a face which
creates the minimum pressure. What is this pressure?
The blocks in the following diagram has a weight of 1500 N.
Find minimum pressure for block A and maximum pressure
for block B.
Block B
Block A
FLUID Pressure
1. Which of the following will have
the greatest pressure?
3. The pressure on the
dam at the bottom of the
reservoir depends on the
(a) Water depth
(b) Water volume
(c) Water mass
(d) length of reservoir
2. What happens to atmospheric
pressure as you go higher (increase
altitude)?
(a) No effect
(c) increase
(b) decrease
(d) balanced
4. Which hole
will shoot out
water with a
larger force?
Liquids incompressible and changes are
transmitted instantaneously and uniformly
to all parts
In hydraulics, the relationship between force and area is directly
proportional, meaning that as the area increases, the force also
increases, as described by Pascal's Principle, Force = Pressure x
Area; essentially, a larger area will experience a greater force.
Which of the following statement about the brake system is/are true?
a. The pressure at X is greater than the pressure at Y
b. The front brakes and rear brakes are applied at exactly the same time
c. The liquid labeled L is water
The figure below shows a cylinder fitted with two pistons
A and B of area 3 and 6 cm2. Piston A is pushed by a
force of 8 N. Find the force on piston B.
Pressure due to gas
• Caused by collision of air molecules
• Factors affecting pressure in enclosed gas:
temperature and volume e.g.
• Molecules of gas exert total force of 100 N on
inner wall of sealed globe. Diameter of globe
is 5 cm. Calculate pressure of gas in globe.
Give answer in S.I. unit. (Area sphere = 4∏r^2)
(ans: 12,739 N/m^2)
Archimedes Principle
when an object is completely or
partially immersed in a fluid, the
weight of fluid displaced is equal
to the upthrust.
When the block held by a piece of
string is totally immersed in the
water, the tension in the string will
be:
(a) nil (zero)
(b) equal to the upthrust
(c) less than the force exerted by the
stone
(d) greater than the force exerted by
the stone
• How does sinking occur? unbalanced
force, weight > upthrust
Density of object > density of liquid
Interesting:
Ships have plimsoll lines to indicate level
at which fully loaded ship should float
since different waters have different
densities.
Warm water less dense than cold water
Fresh water less dense than salty water
• Principle of flotation
- A floating body will displace its own
weight of the liquid in which it is
floating
Weight = upthrust
W=mg
D=m/v therefore W= d x V x g
Instruments to measure pressure:
(a) barometer (Hg or aneroid) for
atm
(b) U-manometer for gas
(c) bourdon gauge
Mercury barometer
Sample Problems:
1. A cement block 0.2 m by 0.4 m by 0.6 m rests
on a table. The weight of the cement block is 45
N. Calculate the pressure caused by the block
when it rests on its smallest area. (Ans:563 Pa)
2. A boy dives into the sea for a few minutes at a
depth of 5 m below the surface. If the density of
seawater is 1100 kg/m^3, calculate pressure
caused by seawater alone. (Ans: 55,000 Pa)
Calculate weight of car if a force of 150 N
is applied to F1 of A1 being 0.2 m^2 and
A2 being 0.5 m^2. (Ans:375N)
4. What is the atmospheric pressure at sea
level?
5. A cherry is made by blowing air into a small
piece of balloon rubber and sealing it off.
The cherry is of radius 0.5 cm and the
pressure of air inside is 1.2 x 10^5 Pa.
Calculate force acting on the inner wall of
the cherry. (ans: 38N)
6. A rectangular block of metal weighing 20 N
has dimensions 10 cm x 8cm x 5 cm. What
is the greatest pressure it can exert when
resting on a flat surface? (Ans: 0.5 N/cm^2)
p. 54 textbook # 2 and 4