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:
- Force per unit mass (\( g = \dfrac{W}{m} \))
- 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).
- Gravitational field strength has two equivalent descriptions:
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.