Mass and Weight Notes

Mass

  • Definition: Measure of the quantity of matter in an object at rest relative to the observer.

  • Property: Resists change in motion. The greater the mass, the more difficult it is to change its motion (speed up, slow down, or change direction).

  • Nature: Scalar quantity (magnitude but no direction).

  • Units: Kilograms (kg).

    • Sometimes given in grams (g), but conversion to kilograms is needed for calculations.

    • 1000 \text{ g} = 1 \text{ kg}

    • 1 \text{ g} = 0.001 \text{ kg}

    • To convert grams to kilograms, divide the mass in grams by 1000.

    • To convert kilograms to grams, multiply the mass in kilograms by 1000.

Weight

  • Definition: Gravitational force on an object with mass.

  • Nature: Vector quantity (both magnitude and direction).

  • Units: Newtons (N).

Weight & Gravity (Extended Tier Only)

  • Weight is the effect of a gravitational field on a mass.

  • Definition: The force acting on an object with mass when placed in a gravitational field.

  • Planets have strong gravitational fields, attracting nearby masses with a strong gravitational force.

  • Because of weight:

    • Objects stay firmly on the ground.

    • Objects will always fall to the ground.

    • Satellites are kept in orbit.

Common Confusions

  • Mass and weight are often used interchangeably in everyday speech, but they have different meanings in Physics.

    • Mass: Amount of matter in an object, scalar quantity, measured in kg.

    • Weight: Force, vector quantity, measured in N.

Gravitational Field Strength

  • Definition: The force per unit mass acting on an object in a gravitational field.

  • On Earth, this is approximately 9.8 \text{ N/kg}.

  • Formula:

    • g = \frac{W}{m}

      • Where:

        • g = gravitational field strength (N/kg)

        • W = force of weight (N)

        • m = mass of object (kg)

Free Fall and Gravitational Field Strength

  • In a vacuum and uniform gravitational field, an object in free fall accelerates at a rate known as g.

  • g = 9.8 \text{ m/s}^2

  • Gravitational field strength and acceleration of free fall are equivalent quantities.

Mass vs. Weight

  • An object’s mass remains constant regardless of its location in the Universe.

  • Weight varies depending on the strength of the gravitational field.

  • Example:

    • The gravitational field strength on the Moon is approximately 1.63 \text{ N/kg}, so an object’s weight will be about 6 times less than on Earth.

Example Calculation: Comparing Weight on Earth and the Moon

  • NASA's Artemis mission aims to send the first woman astronaut to the Moon.

  • Isabelle has a mass of 42 \text{ kg}.

  • Comparison of Isabelle's weight on Earth and the Moon:

    • Gravitational field strength on Earth, g_E = 9.8 \text{ N/kg}.

    • Gravitational field strength on the Moon, g_M = 1.6 \text{ N/kg}.

  • Formula:

    • W = mg

  • Weight on Earth:

    • W_E = 42 \times 9.8 = 411.6 \text{ N} \approx 410 \text{ N} (2 s.f.)

  • Weight on the Moon:

    • W_M = 42 \times 1.6 = 67.2 \text{ N} \approx 67 \text{ N} (2 s.f.)

  • Conclusion:

    • Weight is greater on Earth due to its larger gravitational field strength.

Using a Balance

  • The weight of two objects can be compared using a balance.

  • Since the gravitational field strength is constant on Earth, balances can measure mass.

  • Formula:

    • m = \frac{W}{g}

  • Balances can be digital or analogue.

  • The object is placed on the balance, and the reading gives mass in kg or g.

Force Meters (Newton Meters)

  • Consist of a spring and hook.

  • The object is hung from the hook, and the reading gives weight in N.

Value of 'g'

  • Remember that g = 9.8 \text{ N/kg} and use it in calculations.