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CIE iGCSE Co-ordinated Sciences-P1.3 Mass and weight- Study Notes- New Syllabus

CIE iGCSE Co-ordinated Sciences-P1.3 Mass and weight – Study Notes

CIE iGCSE Co-ordinated Sciences-P1.3 Mass and weight – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.

Key Concepts:

Core

  • State that mass is a measure of the quantity of matter in an object
  • State that weight is the gravitational force on an object that has mass
  • Define gravitational field strength g as the gravitational force per unit mass; recall and use the equation $g = \frac{W}{m}$ and know that near to the surface of the Earth, g is approximately 9.8 N/kg

Supplement

  • Describe, and use the concept of, weight as the effect of a gravitational field on a mass
  • Know that gravitational field strength is equivalent to the acceleration of free fall

CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics

Mass

Mass is a measure of the quantity of matter present in an object.

  • Nature: It is a fundamental scalar quantity (only magnitude, no direction).
  • SI Unit: kilogram (kg).

Properties of Mass:

    • Mass is the same everywhere – it does not depend on location (Earth, Moon, or space).
    • Mass is related to inertia — the greater the mass, the greater the resistance to a change in motion.
    • Mass is different from weight. Weight depends on gravity, but mass does not.

Instruments Used: Mass is measured using a beam balance or electronic balance.

Worked Example:

A rock has a mass of \( 5~\text{kg} \). If the rock is taken from Earth to the Moon, what is its mass there?

▶️ Answer/Explanation

Mass is a measure of the amount of matter in an object and is independent of location.

Therefore, even on the Moon, the mass of the rock remains:

\( \boxed{5~\text{kg}} \)

Weight

Weight is the gravitational force acting on an object that has mass.

  • Nature: It is a vector quantity (has both magnitude and direction).
  • SI Unit: newton (N).

Formula: $ W = m \times g $

where:

    • \( W \) = weight (N)
    • \( m \) = mass of the object (kg)
    • \( g \) = gravitational field strength (\( \text{N/kg} \)), about \( 9.8~\text{N/kg} \) on Earth

Properties of Weight:

    • Weight depends on both the mass of an object and the gravitational field strength at its location.
    • Unlike mass, weight changes from place to place (e.g., Earth vs. Moon).
    • Always acts vertically downwards towards the center of the Earth (or any planet).

Instruments Used: Weight is measured using a spring balance or a newton meter.

Example:

A student has a mass of \( 50~\text{kg} \). Calculate their weight on Earth, where \( g = 9.8~\text{N/kg} \).

▶️ Answer/Explanation

Using the formula: \( W = m \times g \)

\( W = 50 \times 9.8 \)

\( W = 490~\text{N} \)

Therefore, the student’s weight on Earth is \( \boxed{490~\text{N}} \).

Gravitational Field Strength (g)

Gravitational field strength, \( g \), is the gravitational force per unit mass acting on an object.

Formula: $ g = \dfrac{W}{m}$

where:

    • \( g \) = gravitational field strength (\( \text{N/kg} \))
    • \( W \) = weight of the object (N)
    • \( m \) = mass of the object (kg)
  • SI Unit: newton per kilogram (\( \text{N/kg} \)).
  • Nature: It is a vector quantity — it has both magnitude and direction (always directed towards the center of the Earth or planet).

Value near Earth’s surface:

    • Approximately \( 9.8~\text{N/kg} \).
    • Often rounded to \( 10~\text{N/kg} \) for easier calculations.

Key Points:

    • \( g \) is nearly constant on the surface of Earth but varies slightly with altitude and location.
    • On the Moon, \( g \) is smaller (about \( 1.6~\text{N/kg} \)).

Example:

An astronaut has a mass of \( 80~\text{kg} \). On the Moon, their weight is \( 128~\text{N} \). Calculate the gravitational field strength on the Moon.

▶️ Answer/Explanation

Using the formula: \( g = \dfrac{W}{m} \)

\( g = \dfrac{128}{80} \)

\( g = 1.6~\text{N/kg} \)

Therefore, the gravitational field strength on the Moon is \( \boxed{1.6~\text{N/kg}} \).

Gravitational Field Strength and Free Fall

Gravitational field strength (\( g \)) is equivalent to the acceleration of free fall.

Explanation:

    • When an object is in free fall (falling under gravity alone, with no air resistance), it accelerates towards the Earth.
    • The value of this acceleration is exactly the same as the gravitational field strength at that location.
    • On Earth’s surface: $ g \approx 9.8~\text{N/kg} = 9.8~\text{m/s}^2 $

Important Notes:

    • Gravitational field strength has two equivalent descriptions:
      1. Force per unit mass (\( g = \dfrac{W}{m} \))
      2. Acceleration of a freely falling object
    • This means all objects in free fall accelerate at the same rate, regardless of their mass (if air resistance is neglected).

Example:

A ball is dropped from rest near the Earth’s surface. After \( 3~\text{s} \), its speed is found to be \( 29.4~\text{m/s} \). Use this information to determine the acceleration of free fall.

▶️ Answer/Explanation

Acceleration is given by:

\[ a = \dfrac{\Delta v}{t} \]

\( a = \dfrac{29.4}{3} = 9.8~\text{m/s}^2 \)

Thus, the acceleration of free fall is \( \boxed{9.8~\text{m/s}^2} \), which equals the gravitational field strength near Earth’s surface.

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