1. Thrust and Pressure
Thrust
A force acting perpendicular (at right angle) to the surface of an object is called thrust. Its SI unit is Newton (N).
Pressure
The thrust acting per unit area of a surface is called pressure. Pressure = Thrust / Area. The SI unit of pressure is Pascal (Pa), which is equal to Newton per square metre (N/m^2).
Figure 8.1-8.3: Pressure exerted by a solid (brick on foam), a liquid (water in a pipe) and a gas (air on a postcard).
Very Important for SEE: Remember the formula P = F/A and its SI unit Pascal (Pa).
Fluids
Liquids and gases can flow easily, so they are called fluids. Like solids, fluids also exert pressure. A fluid exerts pressure not only on the bottom of its container but on all the walls of the container.
- Fluids exert pressure on the bottom and on all the walls of the container.
- A balloon placed in water experiences an upward force due to water pressure.
- A balloon filled with hydrogen or helium flies upward due to air pressure.
2. Transmission of Pressure
In Solids
Molecules in a solid are packed very close together and do not change position. So, when force is applied on one side of a solid, the pressure generated is not transmitted throughout the solid.
In Liquids and Gases
Structure of molecules in solid, liquid and gas, and compression of fluid in a closed syringe.
Molecules in liquids and gases can move. Liquid molecules are very close together and cannot be pushed much closer, so a liquid cannot be compressed. Because of this, pressure applied at any point in a liquid kept in a closed vessel is transmitted equally in all directions.
Gas molecules have larger spaces between them, so gas can be compressed. Pressure is transmitted in a compressed gas, but not as effectively as in a liquid.
- Solids: pressure is NOT transmitted throughout the object.
- Liquids: pressure is transmitted equally and instantly in all directions (liquids cannot be compressed).
- Gases: pressure is transmitted only after the gas is sufficiently compressed.
3. Pascal's Law
Statement of Pascal's Law
Pascal's law states that when a force is exerted at a point in an enclosed liquid, the pressure generated is transmitted equally in all directions throughout the liquid.
Verification of Pascal's law using a closed circular vessel with four pistons A, B, C and D, each showing equal 10 Pa pressure.
Very Important for SEE: French mathematician Blaise Pascal proposed this law in 1653.
For a vessel with pistons of cross-sectional areas a1, a2, a3, a4 and forces F1, F2, F3, F4 acting on them, Pascal's law gives: F1/a1 = F2/a2 = F3/a3 = F4/a4.
Applications of Pascal's Law
- Hydraulic brakes
- Hydraulic lifts
- Hydraulic presses
- Hydraulic jacks
4. Hydraulic Machine
What is a Hydraulic Machine?
A hydraulic machine is a force-multiplying device based on Pascal's law. It uses an incompressible liquid enclosed between a small piston and a large piston.
Structure of a hydraulic machine showing input force F1 on the small piston and output force F2 on the large piston.
Working Principle and Formula
When force F1 is applied on the small piston of area A1, pressure P1 = F1/A1 is created. According to Pascal's law, this pressure is transmitted equally to the large piston of area A2, so P1 = P2.
Formula: F1/A1 = F2/A2, so F2 = F1 x (A2/A1).
| Symbol | Meaning | SI Unit |
|---|---|---|
| F1 | Force on small piston | N |
| F2 | Force on large piston | N |
| A1 | Area of small piston | m^2 |
| A2 | Area of large piston | m^2 |
Since A2/A1 is always greater than 1, the force is always multiplied when it is transferred from the small piston to the large piston.
Examples of Hydraulic Machines
| Machine | Use |
|---|---|
| Hydraulic lift | Lifting cars or dentist chairs by amplifying a small applied force. |
| Hydraulic brake | Stopping a moving vehicle by transmitting force from a small pedal piston to large wheel pistons. |
| Hydraulic jack | Lifting trucks, buses and cars using a pumping piston and a lifting piston with a one-way valve system. |
| Hydraulic press | Pressing, bending or punching objects such as metal sheets, paper and cotton. |
Hydraulic car lift raising a car on a platform using oil-filled pistons.
Hydraulic brake system in a four-wheeler and a two-wheeler, showing master cylinder, brake fluid and brake pads.
Hydraulic jack with pumping piston, lifting piston and one-way valves.
Numerical Example — Hydraulic Lift
Given: Area of small piston A1 = 0.25 m^2, Area of large piston A2 = 5 m^2, mass of car m = 1200 kg
Required: Force F1 needed on the small piston
Formula: F1/A1 = F2/A2, so F1 = F2 x (A1/A2)
Calculation: F2 = weight of car = mg = 1200 x 9.8 = 11760 N. F1 = 11760 x (0.25/5) = 588 N
Answer: The force required on the small piston is 588 N.
5. Upthrust (Buoyant Force)
What is Upthrust?
An empty bottle being pushed into water, showing the upward force (upthrust) acting on it.
When an object is partially or completely immersed in a fluid (liquid or gas), the fluid pushes it upward. This net upward force exerted by a fluid on an object is called upthrust or buoyant force. Its SI unit is Newton (N).
Upthrust (U) = Actual weight in air (W1) - Apparent weight in liquid (W2)
Cause of Upthrust
A cube immersed in water with pressure arrows on all faces, showing greater pressure on the lower face than the upper face.
A liquid exerts pressure on all sides of an immersed object, and pressure increases with depth. So the pressure (and force) on the lower surface of an object is greater than on the upper surface. Forces on the side surfaces cancel out. The net resulting force acts upward — this is upthrust.
6. Factors Affecting Upthrust
(a) Density of the Liquid
Upthrust is directly proportional to the density of the liquid. A liquid with higher density exerts more upthrust than a liquid with lower density. This is why an iron ball sinks in water but floats on mercury, and an egg floats in salty water but sinks in tap water.
(b) Volume of Liquid Displaced
Upthrust is directly proportional to the volume of liquid displaced by the object. As more of an object is submerged, more liquid is displaced and upthrust increases. Once the object is fully submerged, upthrust remains constant even if depth increases further.
- Upthrust is proportional to density of liquid.
- Upthrust is proportional to volume of liquid displaced.
- Upthrust becomes maximum and constant once the object is completely submerged.
7. Archimedes' Principle
Statement
Verification of Archimedes' principle: a stone weighed in air and in water using a spring balance, with displaced water collected in a eureka can.
Archimedes' principle states that when an object is partially or completely immersed in a liquid, the upthrust on it is equal to the weight of the liquid displaced by it. This principle applies to all fluids, not just liquids.
Very Important for SEE: Greek mathematician Archimedes was born in 287 BC.
Formula: Upthrust (U) = Weight of liquid displaced (W) = mg = V(rho)g, where V is volume of liquid displaced, rho is density of liquid, and g is acceleration due to gravity.
| Symbol | Meaning | SI Unit |
|---|---|---|
| U | Upthrust | N |
| V | Volume of liquid displaced | m^3 |
| rho | Density of liquid | kg/m^3 |
| g | Acceleration due to gravity | m/s^2 |
8. Law of Floatation
Statement
For an object to float in a liquid, the weight of the object must equal the weight of the liquid it displaces. This is called the law of floatation: Weight of object = Weight of liquid displaced.
If the density of an object is less than the density of the liquid, it usually floats. But floating also depends on the shape of the object, because shape affects how much liquid is displaced.
Applications of the Law of Floatation
- Ships and boats: A wide, hollow hull lets a ship displace enough water to generate upthrust equal to its own weight, even though iron is denser than water.
- Submarines: Filling the blast tank with water increases weight so the submarine sinks; blowing water out with compressed air decreases weight so it rises.
- Fish: Filling the swim bladder with air increases body volume and upthrust, helping the fish rise; emptying it helps the fish sink.
- Hydrometer and Lactometer: A hydrometer measures the relative density of liquids; a lactometer (a type of hydrometer) tests the purity of milk by checking water content.
- Balloons: A helium or hydrogen balloon rises because it is lighter than the air it displaces; it floats when weight equals upthrust.
- Hot air balloons: Heating the air inside reduces its density so the balloon displaces more air than its weight and rises; cooling the air makes it sink.
An iron ship floating on water, showing weight and buoyant force balanced through a wide hollow hull that displaces a large volume of water.
A submarine with ballast tanks, shown rising and sinking in water as fish swim up and down beside it.
Three hot air balloons showing upthrust greater than weight, upthrust equal to weight, and upthrust less than weight.
Important Definitions
- Thrust: Force acting perpendicular to the surface of an object.
- Pressure: Thrust acting per unit area (P = F/A); SI unit Pascal.
- Fluid: A substance that can flow easily, such as a liquid or a gas.
- Upthrust: The net upward force exerted by a fluid on an object immersed in it.
- Pascal's law: Pressure applied at a point in an enclosed liquid is transmitted equally in all directions.
- Archimedes' principle: Upthrust on an immersed object equals the weight of the liquid displaced.
- Law of floatation: An object floats when its weight equals the weight of liquid it displaces.
Important Differences
Difference Between Pressure and Upthrust
| Pressure | Upthrust |
|---|---|
| Thrust acting per unit area of a surface. | Net upward force exerted by a fluid on an immersed object. |
| Can act in any direction depending on the surface. | Always acts vertically upward. |
| SI unit is Pascal (N/m^2). | SI unit is Newton (N). |
Important Formulas
| Concept | Formula |
|---|---|
| Pressure | P = F / A |
| Pascal's law (hydraulic machine) | F1 / A1 = F2 / A2 |
| Upthrust (from weights) | U = W1 - W2 |
| Upthrust (Archimedes) | U = V x rho x g |
| Law of floatation | Weight of object = Weight of liquid displaced |
Common Mistakes in SEE
- Do not confuse thrust (force) with pressure (force per unit area).
- Do not forget that pressure in a liquid is transmitted equally in all directions, but in a solid it is not transmitted at all.
- Do not write upthrust formula as W1 + W2 — it is always W1 minus W2 (actual weight minus apparent weight).
- Remember: floating depends on both density AND shape of the object, not density alone.
- Always use SI units (N, Pa, m^2, kg/m^3) in numerical answers.
- In hydraulic machine problems, always check which piston is 'small' (input) and which is 'large' (output) before applying the formula.
Quick Revision
- Pressure = Force / Area; SI unit Pascal (N/m^2).
- Solids do not transmit pressure; liquids transmit it equally in all directions; gases transmit it only after compression.
- Pascal's law: pressure at a point in an enclosed liquid is transmitted equally everywhere.
- Hydraulic machine formula: F2 = F1 x (A2/A1) — force gets multiplied.
- Upthrust = Actual weight - Apparent weight = Weight of liquid displaced.
- Archimedes' principle: U = V x rho x g.
- Law of floatation: Weight of object = Weight of liquid displaced.
- Upthrust depends on density of liquid and volume of liquid displaced.
- Ships float due to shape (wide hollow hull); submarines and fish control sinking/rising using ballast/air bladder.