Gravitational Force, Mass, and Weight

Gravitational Force and Field Strength

• Direction of Gravitational Force:

  • The gravitational force of the Earth pulls all objects towards the centre of the Earth.

• Definition of Weight:

  • Weight is the gravitational force exerted by the Earth on an object.

• Gravitational Field Strength ($g$):

  • Definition: Gravitational field strength is defined as the amount of gravitational force acting per unit mass on a $1\,kg$ mass.

  • Symbol: Denoted by the symbol $g$.

  • Value on Earth: The gravitational field strength on Earth has a value of $10\,N/kg$.

• Weight of a $1\,kg$ Mass on Earth:

  • The weight of an object with a mass of $1\,kg$ on Earth is $10\,N$.

Mathematical Relationship Between Mass, Weight, and Gravitational Field Strength

• Distinction Between Mass and Weight:

  • Mass and weight are fundamentally distinct physical quantities ($\text{MASS} \neq \text{WEIGHT}$).

• Formula for Weight:

  • The weight of an object is calculated using the equation:     $W = m \times g$

  • Description of variables:

  • $W$ = weight or gravitational force acting on the object (measured in Newtons, $N$).

  • $m$ = mass of the object (measured in kilograms, $kg$).

  • $g$ = gravitational field strength (measured in Newtons per kilogram, $10\,N/kg$ on Earth).

Fundamental Properties of Mass

• Definition:

  • Mass is a measure of the amount of substance (or matter) in a body.

• S.I. Unit:

  • The Standard International (S.I.) unit of mass is the kilogram ($kg$).

• Constancy Across Locations:

  • Mass does not change with location; it remains constant regardless of where the object is situated.

• Measuring Apparatus:

  • The measuring apparatus used to determine mass are the beam balance or the electronic balance.

Fundamental Properties of Weight

• Definition:

  • Weight is the gravitational force acting on an object.

• S.I. Unit:

  • The Standard International (S.I.) unit of weight is the Newton ($N$).

• Variability with Location:

  • Weight may change with location based on variations in gravitational field strength.

• Measuring Apparatus:

  • The measuring apparatus used to determine weight is the spring balance.

Differences Between Mass and Weight

• Definition:

  • Mass: The amount of matter in a body.

  • Weight: The gravitational force acting on a body.

• Dependence on Location:

  • Mass: Remains constant regardless of location.

  • Weight: Varies according to the gravitational field strength of the location.

• Measuring Instrument:

  • Mass: Measured using a beam balance or an electronic balance.

  • Weight: Measured using a spring balance.

• S.I. Unit:

  • Mass: Kilogram ($kg$).

  • Weight: Newton ($N$).