Thrust: When a force acts on a surface, the part of the force acting perpendicular (at right angles) to that surface is called thrust. Thrust is simply a force, so its SI unit is the newton (N). Standing on soft sand, your weight acts as thrust pushing down on the ground.
Pressure: What matters for many effects is not the total thrust but how it is spread out. Pressure is the thrust acting per unit area: $P = \dfrac{F}{A}$. Its SI unit is the pascal (Pa), where $1\ \text{Pa} = 1\ \text{N/m}^2$. The same force on a smaller area gives a larger pressure — that is why a sharp knife (tiny edge area) cuts easily, why a camel's broad feet stop it sinking in sand, and why a sharp nail pierces wood while a blunt one does not.
Pressure in fluids: Liquids and gases (together called fluids) exert pressure on the walls and base of their container and on anything submerged in them. Important facts:
- Fluid pressure acts in all directions, not just downward.
- Pressure increases with depth — deeper water pushes harder, which is why dam walls are built thicker at the bottom.
- At the same depth in the same fluid, the pressure is the same in every direction.
Buoyancy (upthrust): When an object is placed in a fluid, the fluid pushes up on it with a force called the buoyant force or upthrust. This is why a bucket feels lighter when lowered into a well, and why we feel lighter in a pool. The buoyant force acts upward and opposes the object's weight.
Archimedes' Principle: When a body is wholly or partly immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. The upthrust equals $\rho_{fluid} \cdot V_{displaced} \cdot g$. This single idea explains ships, submarines and hot-air balloons.
Density and relative density: Density is mass per unit volume, $\rho = \dfrac{m}{V}$, with SI unit $\text{kg/m}^3$. Relative density is the ratio of a substance's density to the density of water: $\text{R.D.} = \dfrac{\rho_{substance}}{\rho_{water}}$. Being a ratio, it has no units. Water's density is $1000\ \text{kg/m}^3$ ($1\ \text{g/cm}^3$), so mercury (R.D. $= 13.6$) is 13.6 times as dense as water.
Why objects float or sink: Compare the object's density with the fluid's:
- Density greater than the fluid's → weight beats upthrust → it sinks (an iron nail).
- Density less than the fluid's → upthrust wins → it floats, sinking only until it displaces its own weight of fluid (a cork, or a hollow steel ship).
- Densities equal → it floats fully submerged in balance.
A force of $200\ \text{N}$ acts perpendicularly on a surface of area $4\ \text{m}^2$. Find the pressure exerted.
Solution- Pressure formula: $P = \dfrac{F}{A}$.
- Here $F = 200\ \text{N}$ (thrust) and $A = 4\ \text{m}^2$.
- $P = \dfrac{200}{4} = 50\ \text{Pa}$.
Answer: The pressure is $50\ \text{Pa}$ (i.e. $50\ \text{N/m}^2$).
Explain why the same person sinks into soft snow while walking in shoes but not while wearing wide skis.
Solution- The person's weight (thrust) is the same in both cases.
- Pressure $P = \dfrac{F}{A}$ depends on the area in contact with the snow.
- Shoes have a small area, so the pressure on the snow is large and the feet sink in.
- Skis spread the same weight over a much larger area, so the pressure is small and the snow supports the person.
Answer: Wide skis increase the contact area $A$, lowering the pressure $P = F/A$ so the person does not sink.
A block of metal has a mass of $270\ \text{g}$ and a volume of $100\ \text{cm}^3$. Find its density and its relative density. (Density of water $= 1\ \text{g/cm}^3$.)
Solution- Density: $\rho = \dfrac{m}{V} = \dfrac{270}{100} = 2.7\ \text{g/cm}^3$.
- In SI units this is $2700\ \text{kg/m}^3$.
- Relative density: $\text{R.D.} = \dfrac{\rho_{substance}}{\rho_{water}} = \dfrac{2.7}{1} = 2.7$.
- R.D. is a ratio, so it has no units.
Answer: Density $= 2.7\ \text{g/cm}^3$ ($2700\ \text{kg/m}^3$); relative density $= 2.7$ (this is aluminium).
State Archimedes' principle and use it to explain why a huge steel ship floats while a small steel nail sinks.
Solution- Archimedes' principle: a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
- A solid nail has high density; it displaces only a little water, so the upthrust is less than its weight and it sinks.
- A ship is hollow, so its overall (average) density is much less than water's.
- The ship sinks just far enough to displace a weight of water equal to its own weight, so the upthrust balances the weight and it floats.
Answer: Shape matters: the hollow ship displaces enough water for the buoyant force to equal its weight; the dense nail cannot, so it sinks.
An object weighs $50\ \text{N}$ in air and $40\ \text{N}$ when fully immersed in water. Find the buoyant force on it and the weight of water displaced.
Solution- The apparent loss in weight equals the buoyant force (upthrust).
- Loss in weight $= 50 - 40 = 10\ \text{N}$.
- So the buoyant force $= 10\ \text{N}$.
- By Archimedes' principle, the weight of water displaced equals this upthrust $= 10\ \text{N}$.
Answer: Buoyant force $= 10\ \text{N}$; weight of displaced water $= 10\ \text{N}$.
A wooden cube of side $10\ \text{cm}$ and density $600\ \text{kg/m}^3$ is placed in water (density $1000\ \text{kg/m}^3$). Will it float or sink, and why?
Solution- Compare densities: the cube's density is $600\ \text{kg/m}^3$, water's is $1000\ \text{kg/m}^3$.
- Since the cube's density ($600$) is less than water's ($1000$), it floats.
- Physically, the maximum upthrust (when fully submerged) would exceed the cube's weight, so it rises until only part is submerged.
- It floats with the fraction submerged $= \dfrac{600}{1000} = 0.6$, i.e. 60% of the cube is under water.
Answer: It floats (its density is less than water's), with about 60% of its volume submerged.