Understanding Pressure, Buoyancy, and Archimedes' Principle in Physics

PRESSURE
 Pressure is defined as the force applied perpendicular
to the surface of an object per unit area.
 It is calculated using the formula: P=
 Where;
P- Pressure
F- Force
A- Surface area

PRESSURE
Standard metric units are Pascals (Pa)
Where 1 Pa = 1
Two common types of pressure problems are
Solid Pressure and Fluid (Hydrostatic) Pressure.

1. SOLID PRESSURE (FORCE OVER AREA)
This type of problem measures how a specific
force (like weight) distributes over a surface.
Problem 1: A heavy crate weighing 150N rests on a horizontal
floor. The bottom of the crate is a rectangle measuring 2m by
1.5m. What pressure does crate exert on the floor?
1. Identify the given data:
Force (F) = 150N
Area (A) =
2. Apply the formula: 3. Solution:
P=

2. FLUID PRESSURE (DEPTH AND DENSITY)
This type of problem determines the pressure
exerted by a liquid at a specific depth. The
formula is P= .
Where:
p- is the fluid density
g- is gravitational acceleration ()
h- is depth.

2. FLUID PRESSURE (DEPTH AND DENSITY)
Problem: A swimming pool is filled with water to a depth of 3
meters. Calculate the water pressure at the bottom of the pool.
Given, density of water is and gravitational acceleration is .
1. Identify the given data:
Density (p) =
Gravitational acceleration (g)=
Depth (h) = 3 meters
2. Apply the formula:
3. Solution:
P= 3 meters
P = 29, 400 Pa

ACTIVITY
1. A force of is applied to a hydraulic piston with a surface area
of . What is the resulting pressure inside the fluid?
2. A confined fluid is pressurized to 80 Pa. If this fluid acts on a
piston with an area of 0.5 , what is the total force exerted?
3. An output force of 600N is generated by a hydraulic cylinder
operating a pressure of 120Pa. What is the surface area of the
cylinder’s piston?
4. A small hand pump applies a force of 18N over a tiny piston
area of 0.3 . What is the pressure transmitted to the fluid?
5. A heavy-duty hydraulic press operates at a constant pressure
of 400 Pa. If the press piston has a surface area of 2.5 , what is
the total force it can output?

Exercise
1. A 2000-lb car is lifted by a manually
operated hydraulic lift. The area of the
shaft of the lift is 80 , the area of the piston
that forces liquid into the system is . What
force must be exerted on the piston to lift
the car?

Exercise
2. An engineering student wants to build a
hydraulic pump to lift a 1,825N crate. The
pump will have two pistons connected via a
fluid chamber. The student calculates that a
force of 442N will be exerted on the small
piston, which will have an area of 50.2 . What
must the area of the large piston be to exert
the desired force?

Exercise
3. A mechanic is designing a hydraulic lift to raise
a 2,400-N motorcycle. The lift will have two pistons
connected by a sealed chamber filled with oil. The
mechanic can apply a force of 300 N on the small
piston, which has an area of 12 cm². What must
the area of the large piston be to lift the
motorcycle?

ACTIVITY
1. A mechanic is using a hydraulic lift to raise a 4,500-N car. The lift has two pistons
connected by a fluid chamber. The area of the large piston is 180 cm², while
the area of the small piston is 12 cm². What force must be exerted on the small
piston to lift the car?
2. A construction worker uses a hydraulic jack to lift a 9,600-N concrete slab. The
large piston has an area of 320 cm², while the small piston has an area of 16
cm². What force must be applied to the small piston to lift the slab?
3. A factory worker is designing a hydraulic press to lift a 6,000-N metal block. The
press uses two pistons connected by a sealed fluid chamber. The worker can
apply a force of 300 N on the small piston, which has an area of 15 cm². What
must the area of the large piston be to produce the required lifting force?
4. An engineering student is building a hydraulic lift to raise a 10,000-N machine.
The student can exert a force of 500 N on the small piston, which has an area
of 20 cm². What must the area of the large piston be to exert the desired force?

Buoyancy and
Archimedes’
Principle

BUOYANCY
Have you ever tried to push a beach ball
underwater? What happened?
this magical force called buoyant force
It pushes back and floats up

BUOYANCY
Buoyant force: It’s the upward force that fluids like
water or air give to anything placed in them.
If an object pushes aside (displaces) some fluid, the
fluid pushes back with a force equal to the weight of
the fluid displaced.

But why does this force happen?
The deeper you go in a fluid, the more pressure it has.
The water underneath an object pushes harder than the
water above it.
This creates an upward force
That's the buoyant force.
Fluids don’t just sit there—they’re constantly
applying pressure in all directions.

Q: Why do some things, like a stone, sink instead of
float?
It all depends on a battle of forces—who's stronger?
Weight: The downward pull of gravity.
Buoyant Force: The upward push from the fluid.
If the object’s weight wins = it sinks.
If buoyant force wins = it floats.

Density and Buoyant Force
Density: the amount of mass in a given volume.
If the average density is …
… equal to water, the object will float.
… greater than water, the object will sink.
… less than water, the object will rise.
More dense = heavier.
Less dense = lighter.

Density and Buoyant Force
Ice: is less dense than water.
That’s why ice floats along the ocean surface.
Oil: is less dense than water.
So oil floats instead of mixing in water.
Helium: is less dense than air.
That’s why your birthday balloons float to the
ceiling.
https://simpop.org/buoyancy/buoyancy.htm

Buoyant Force
Buoyancy force depends upon two factors:
Amount (Volume) of liquid displaced by the object
The density of the object.

Object Displaced Water Buoyant Push Sink/Float
Iron nail Very little Very weak Sinks
Steel ship Tons Very strong Floats
Buoyant Force
Buoyancy force depends upon two factors:
Amount (Volume) of liquid displaced by the object
The density of the object.

ARCHIMEDES’ PRINCIPLE
Any object completely or partially submerged in a fluid
experiences an upward force equal in
magnitude to the weight of the fluid displaced by the
object.

Force Balance Inside a Fluid
An object submerged in a fluid feels two main forces:
• Gravity (its weight) pulling it downward
• Buoyant force (upthrust) pushing it upward due to fluid
pressure differences.
The object’s apparent weight is the net force
after upthrust partially cancels out gravity.
Apparent weight= Weight of object (in the air) – Thrust force
(buoyancy)

The “weight lost” when an object enters a fluid is exactly equal to
the weight of the fluid displaced.
apparent weight loss = weight of fluid displaced

•ρ is the density (in kg/m³ or g/cm³),
•V is the volume (in m³ or cm³).
•g is the gravity ( in Newton per kilogram (N/kg))
•m is the mass (in kg or g),
ARCHIMEDES’ PRINCIPLE FORMULA
Formula: Buoyant Force = ρ × V × g
ρ = density of fluid | V = volume displaced | g = gravity

Archimedes’ Principle Derivation
Weight = mass x acceleration due to the
gravity
Weight = mass x gravity
Weight = density x volume x gravity
mass = density x volume
From Archimedes’ principle, we know that
the apparent loss of weight is equal to the
weight of the water displaced therefore the
thrust force is given by the following
equation:
Formula: Buoyant Force = ρ × V × g
ρ = density of fluid | V = volume displaced | g = gravity

Wood has density of 0.53 g/.
What is the volume of 33.3 g of wood?
Given
density = 0.53 g/
mass = 33.3 g
volume = ?
=
V = = 62.8

Term Definition
Actual Weight Force of gravity on the object in air
Buoyant Force Upward force equal to weight of displaced fluid
Apparent Weight What you feel in the fluid: gravity – buoyant force
Displaced Fluid Fluid volume equal to object’s submerged volume
Archimedes’ Law Buoyant force = Weight of displaced fluid

Understanding Pressure, Buoyancy, and Archimedes' Principle in Physics

Understanding Pressure, Buoyancy, and Archimedes' Principle in Physics