The nature of gravitational force and weight

Gravitational force is the attractive force that pulls objects with mass toward each other. On Earth, this force is most evident as the pull toward the planet's center. Weight is defined as the gravitational force acting on an object, which depends on both the object's mass and the strength of the gravitational field at its location.

This force causes objects to accelerate toward the ground when dropped. Weight acts downward and is a vector quantity, meaning it has both magnitude and direction.

The difference between mass and weight

Mass and weight are related but distinct concepts in physics. Mass refers to the amount of matter in an object, which remains constant regardless of location. Weight, however, is the gravitational force on that object, which can change based on the gravitational field strength.

Key differences between mass and weight

For example, an object with a mass of 5 kg will have the same mass on Earth or the Moon, but its weight will be different in each place due to varying gravitational pull.

How weight varies by location while mass remains constant

Weight varies because it depends on gravitational field strength (g), which is the measure of gravitational force per unit mass at a specific location, expressed in newtons per kilogram (N/kg). On Earth, g is approximately 9.8 N/kg, but it is weaker on the Moon (about 1.6 N/kg) and stronger on Jupiter (about 24.8 N/kg).

Mass stays constant because it is an intrinsic property of the object, not affected by external forces. This distinction is important for understanding why astronauts feel "weightless" in space but retain their mass.

Formula for weight

$W=mg$

Where:

• W = Weight (N)
• m = Mass (kg)
• g = Gravitational field strength (N/kg)

This equation shows the direct relationship: weight increases with mass or with stronger gravitational fields.

Worked example - Calculating weight on different locations

An object has a mass of 10 kg. Calculate its weight on Earth where g = 9.8 N/kg and on the Moon where g = 1.6 N/kg.

Step 1: Formula

$W=mg$

Step 2: Calculation on Earth

$W=10\times 9.8=98\text{ N}$

Step 3: Calculation on the Moon

$W=10\times 1.6=16\text{ N}$

Step 4: Interpretation

The object's weight is 98 N on Earth and 16 N on the Moon, while its mass remains 10 kg in both locations.

What gravitational potential energy is and how it is stored

Gravitational potential energy (GPE) is the energy stored in an object due to its position in a gravitational field, such as being raised above the ground on Earth. When an object is lifted against gravity, work is done to overcome the gravitational force, and this energy is stored as GPE.

The higher an object is positioned, the more GPE it has, because more energy was required to lift it there. If the object falls, this stored energy is converted into kinetic energy.

The formula for calculating gravitational potential energy

Gravitational potential energy can be calculated using a specific formula that accounts for the object's mass, the gravitational field strength, and its height above a reference point (usually the ground). The result is measured in joules (J), which is the unit of energy.

Formula for gravitational potential energy

$GPE=mgh$

Where:

• GPE = Gravitational potential energy (J)
• m = Mass (kg)
• g = Gravitational field strength (N/kg)
• h = Height (m)

This formula assumes a constant gravitational field near the surface of a planet, like Earth.

How energy required to overcome gravity transfers to an object's gravitational potential energy store

When you lift an object, you apply force to overcome gravity, doing work on the object. This work transfers energy to the object's gravitational potential energy store. The amount of energy transferred equals the GPE gained, as given by the formula GPE = mgh.

For instance, lifting a book onto a shelf requires energy input equal to the book's mass times g times the shelf's height. This stored energy can later be released if the book falls, converting back to other forms like kinetic energy or heat upon impact.

Worked example - Calculating gravitational potential energy

A 2 kg object is lifted to a height of 5 m on Earth, where g = 9.8 N/kg. Calculate the gravitational potential energy stored in the object.

Step 1: Formula

$GPE=mgh$

Step 2: Substitution and calculation

$GPE=2\times 9.8\times 5=98\text{ J}$

Step 3: Interpretation

The object stores 98 J of gravitational potential energy due to its position 5 m above the ground. This energy was transferred by the work done to lift it against gravity.