Gravitation

The One Thing

Gravitation acts between all masses and explains free fall, while thrust, pressure and buoyancy describe how forces act on surfaces and within fluids. Whether an object floats or sinks depends on the balance between its weight and the buoyant force, together with the relative densities of the object and fluid.

Reactions, Processes and Experiments

Key Terms

• Gravitation: The force of attraction between any two objects having mass.
• Universal law of gravitation: The force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
• Gravitational force: The attractive force acting between two masses, given by F = Gm1m2/r^2.
• Universal gravitational constant (G): A constant of proportionality in the law of gravitation; its value is approximately 6.67 × 10^-11 N m^2 kg^-2.
• Free fall: The motion of an object when it falls under the influence of gravity alone.
• Acceleration due to gravity (g): The acceleration of a freely falling object caused by Earth’s gravity; near Earth’s surface it is approximately 9.8 m/s^2.
• Mass: The amount of matter in an object. It remains constant at different places and is measured in kilograms.
• Weight: The force with which Earth attracts an object, given by W = mg. Weight changes when the value of g changes.
• Thrust: The force acting normally, or perpendicular, to a surface.
• Pressure: Thrust acting on unit area of a surface, given by P = thrust/area.
• Pascal: The SI unit of pressure. One pascal equals one newton per square metre.
• Buoyant force: The upward force exerted by a fluid on an object partially or completely immersed in it.
• Archimedes’ principle: An object immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by the object.
• Relative density: The ratio of the density of a substance to the density of water at the same conditions; it has no unit.
• Density: Mass per unit volume, given by density = mass/volume.
• Flotation: The condition in which an object remains on the surface of a fluid because the buoyant force balances its weight.

Easily Confused

• Mass and weight: Mass is the amount of matter and remains constant; weight is the gravitational force W = mg and varies when g changes.
• Thrust and pressure: Thrust is the perpendicular force itself; pressure is thrust per unit area, P = F/A.
• Gravitation and gravitational force: Gravitation is the general attraction between masses; gravitational force is the force between particular masses, given by F = Gm1m2/r^2.
• Free fall and upward motion under gravity: Free fall refers to motion when gravity alone acts, including downward falling; an upwardly thrown object also accelerates downward because of gravity.
• Buoyant force and flotation: Buoyant force is the upward force exerted by a fluid; flotation occurs when that force balances the object’s weight.
• Density and relative density: Density is mass per unit volume and has units; relative density is the ratio of a substance’s density to water’s density and has no unit.
• Sinking and floating: An object sinks when its weight is greater than the buoyant force; it floats when the buoyant force balances its weight.
• Object density and average density of a ship: A hollow ship can float even when its materials are denser than water because its overall average density, including the air inside, is less than water’s density.
• Acceleration and velocity at the highest point: At the highest point of upward motion, velocity is zero, but acceleration due to gravity is still present and directed downward.
• Value of $g$ in different locations: $g$ is slightly greater near the poles, slightly smaller near the equator, and decreases with altitude.

What Gets Asked

• State or apply the universal law of gravitation: Use F = Gm1m2/r^2, identify the masses and the distance between their centres, and remember that the force increases with either mass but decreases as distance increases.
• Solve free-fall and vertical-motion problems: Select the appropriate equation, such as v = u + gt, s = ut + 1/2 gt^2, or v^2 - u^2 = 2gs for downward motion; for upward motion use v = u - gt and h = ut - 1/2 gt^2.
• Distinguish mass from weight: Use W = mg and state that mass remains unchanged on the Moon while weight is about one-sixth of its Earth value.
• Calculate or compare pressure: Use P = F/A and identify whether changing the area increases or decreases pressure; examples include sharp knives, pointed nails, broad school-bag straps, and wide building foundations.
• Explain buoyancy and flotation: Apply Archimedes’ principle and compare weight with buoyant force: weight greater than buoyant force means sinking, equality means floating, and buoyant force greater than weight means rising.
• Explain why a hollow ship floats or calculate relative density: Use average density for flotation and Relative density = density of substance/density of water; do not confuse relative density with density, since relative density has no unit.