JAMB Physics · Section A
Study notes for Liquids At Rest — part of the JAMB UTME Physics syllabus. 6 learning objectives with explanations and exam tips.
Density tells you how much mass is packed into a certain volume of something. Think of it as how tightly packed the particles are. The formula is density equals mass divided by volume. A substance with high density means its particles are squeezed close together, while low density means they're spread out.
Consider palm oil and water. Water is denser than palm oil, which is why oil floats on top when you mix them in a container. This happens because water particles are more tightly packed than oil particles. Another example is how a piece of iron sinks in water but cork floats—iron is much denser than water while cork is less dense.
Understanding density helps explain why objects sink or float in liquids. Different substances have different densities, and this property is crucial for many practical applications in physics.
When you place an object in water, the liquid pushes upward against it with a force called upthrust or buoyancy. This happens because water pressure increases with depth, so the pressure pushing up from below is stronger than the pressure pushing down from above. The upthrust equals the weight of liquid displaced by the object—this is Archimedes' principle.
Think of a floating canoe on the Lagos lagoon. The canoe displaces water equal to its weight, and the upthrust from that displaced water supports it perfectly. If you add too many passengers, the canoe sinks deeper until it displaces enough water to balance everyone's weight. Remove passengers, and it floats higher.
The formula is straightforward: Upthrust = ρ × V × g, where ρ is liquid density, V is volume displaced, and g is gravity (9.8 m/s²).
When an object is completely immersed in a liquid, it experiences an upward force called buoyancy. Think of it like this: imagine pushing a plastic ball underwater in a swimming pool—the water pushes back upward with a force. This happens because the pressure at the bottom of the object is greater than the pressure at the top, creating a net upward push.
The buoyant force equals the weight of liquid displaced by the object. This is Archimedes' principle, discovered over 2,000 years ago. Consider a Nigerian example: when you float a metal pan on water, it displaces water and the buoyant force keeps it afloat. But if you press that same pan underwater without displacing enough water, it sinks because the buoyant force becomes insufficient.
An immersed object experiences three forces: its weight downward, buoyancy upward, and possibly friction. Whether something floats, sinks, or stays suspended depends on comparing these forces.
When you push an object into water, the water pushes back with a force equal to the weight of water displaced. This is Archimedes' principle, and it explains why ships float and why you feel lighter in a swimming pool. The upward force is called buoyancy or upthrust.
Think about a canoe on the River Niger. The canoe displaces water equal to its own weight, so the water pushes up with enough force to keep it floating. If you add too much load, the canoe sinks deeper, displacing more water until the upward force balances the total weight. When weight exceeds the maximum water that can be displaced, the canoe sinks.
This principle applies to all objects in fluids—water or air. Dense objects sink because they displace less water than their weight. Less dense objects float because water pushes them up harder than gravity pulls them down.
When an object floats in water, it's because the upward force from water (buoyancy) equals the weight of the object pushing downward. This balance is what keeps ships, canoes, and even you afloat when swimming. The key idea is density—if something is less dense than water, it floats; if denser, it sinks.
Think about a Lagos ferry boat carrying hundreds of passengers. That heavy steel vessel floats because its overall density (including the air inside) remains less than water's density. If water leaked in and filled that air space, the ferry would sink because total density would increase.
Archimedes' Principle is your foundation here: a floating object displaces a weight of liquid equal to its own weight. This means the volume of water pushed aside must equal enough water to balance the object's mass.
When we measure temperature, we rely on thermometric properties—these are physical characteristics of liquids that change predictably with temperature changes. The most common thermometric property is volume expansion. As temperature increases, the particles in a liquid move faster and take up more space, so the liquid expands. This is why mercury in a clinical thermometer rises when placed under your armpit or in hot water.
Another important thermometric property is density change. When a liquid heats up, it becomes less dense and rises; when it cools, it becomes denser and sinks. Think about how boiling water in a Nigerian pot creates convection currents—the hot water at the bottom rises while cooler water sinks.
The electrical resistance of certain liquids also changes with temperature, making it useful for temperature measurement in industrial settings. These properties work because molecular motion increases with heat, directly affecting how liquids behave physically.