Weight, Mass & Gravity

The Weight Formula: The relationship between mass and weight is defined by the linear equation $W = m \times g$. This shows that weight is directly proportional to both the mass of the object and the strength of the gravitational field it occupies.

Field Strength as Acceleration: In the context of kinematics, $g$ is also known as the acceleration of free fall. In a vacuum, all objects accelerate toward the center of a planet at the same rate regardless of their mass because the ratio of weight to mass is constant ($g = \frac{W}{m}$).

Universal Gravitation: Gravity is an attractive force that exists between any two masses. The strength of a planet's gravitational field depends on its total mass and its radius; larger, denser planets typically exert a stronger pull.

Calculating Weight: To find the weight of an object, identify its mass in kilograms and the local gravitational field strength. Multiply these values to get the force in Newtons ($W = m \cdot g$).

Determining Mass from Weight: If the weight and field strength are known, mass can be calculated using the rearranged formula $m = \frac{W}{g}$. This is useful for determining the quantity of matter when using scales calibrated for specific planets.

Unit Conversion: Physics calculations require mass to be in kilograms (kg). If a value is provided in grams (g), it must be divided by $1000$ before being used in the weight formula.

Check the Units: Examiners often provide mass in grams to test your attention to detail. Always convert to kilograms ($1 \, \text{kg} = 1000 \, \text{g}$) before calculating weight.

Identify the Planet: Read the prompt carefully to determine the value of $g$. While Earth is typically $9.8$ or $10 \, \text{N/kg}$, other celestial bodies will have different values provided in the question data.

Vector Awareness: Remember that weight is a force. If a question asks for the 'force of gravity', it is asking for weight, and the direction is always 'downwards' toward the center of the planet.

Sanity Check: If an object moves from Earth to the Moon, its mass must not change. If your calculation shows a change in mass, you have likely confused the two concepts.

Interchanging Terms: In everyday language, people use 'weight' when they mean 'mass' (e.g., 'I weigh 70 kg'). In physics, this is technically incorrect as kilograms measure mass, not force.

Gravity and Vacuum: A common misconception is that there is no gravity in a vacuum. Gravity exists everywhere there is mass; a vacuum simply means there is no air resistance to oppose the force of gravity.

Weightlessness: Being 'weightless' in orbit does not mean gravity is zero. It means the object is in a state of constant free fall where the support force (normal force) is zero, even though the gravitational force (weight) is still acting.