Mass & Weight (CIE IGCSE Physics)

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Leander

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Physics

Mass & weight

Mass

Mass is defined as:

A measure of the quantity of matter in an object at rest relative to the observer

Consequently, mass is the property of an object that resists change in motion
The greater the mass of an object, the more difficult it is to speed it up, slow it down, or change its direction

Mass is a scalar quantity that has magnitude but no direction
Mass is measured in kilograms (kg)
- Sometimes mass may be given in grams (g) but this will need to be converted to kilograms when used in calculations
  - 1000 g = 1 kg
  - 1 g = 0.001 kg
- To convert g to kg, divide the mass in g by 1000
- To convert kg to g, multiply the mass in g by 1000

Weight

Weight is a gravitational force on an object with mass
Since weight is a force, it is a vector quantity with both magnitude and direction
Weight is measured in newtons (N)

Worked example

An object has a mass of 4.5 kg.

State the mass of the object in grams (g).

Answer:

Step 1: State the conversion between g and kg

1 kg = 1000 g

Step 2: Convert kg into g by multiplying

$m = 4.5 \times 1000$

$m = 4500 g$

Exam Tip

Students commonly confuse mass and weight because the terms are used interchangeably in everyday speech. In Physics, mass and weight mean very different things, and you must be confident that you can explain the difference.

Mass is the amount of matter an object has; it is a scalar quantity, and it is measured in kg.
Weight is a force; it is a vector quantity, and it is measured in N.

Weight & gravity

Extended tier only

Weight and gravitational field strength

Weight is the effect of a gravitational field on a mass
Weight is defined as:

The force acting on an object with mass when placed in a gravitational field

Planets have strong gravitational fields
- Hence, they attract 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

5-1-4-weight-force

Some of the phenomena associated with gravitational attraction and the weight force

Defining gravitational field strength

Gravitational field strength is defined as:

The force per unit mass acting on an object in a gravitational field

On Earth, this is equal to 9.8 N/kg

$g = \frac{W}{m}$

Where:
- $g$ = gravitational field strength, measured in newtons per kilogram (N/kg)
- $W$ = force of weight, measured in newtons (N)
- $m$ = mass of object, measured in kilograms (kg)

An object in free fall in a vacuum, in a uniform gravitational field, will accelerate at a rate also known as
- Where $g$ = acceleration of free fall
- In this context, $g$ = 9.8 m/s²
- Gravitational field strength and acceleration of free fall are equivalent quantities

Mass vs. weight

An object’s mass always remains the same, regardless of its location in the Universe
The weight force exerted on the object will differ depending on the strength of the gravitational field in its location
For example, the gravitational field strength on the Moon is 1.63 N/kg, meaning an object’s weight will be about 6 times less than on Earth

Mass vs weight, downloadable AS & A Level Physics revision notes

On the Moon, a person's mass will stay the same but their weight will be much lower

You can find more information about the gravitational field strength on different planets in the revision note Gravitational field strength

Worked example

NASA's Artemis mission aims to send the first woman astronaut to the Moon. Isabelle hopes to one day become an astronaut. She has a mass of 42 kg.

Compare the difference between Isabelle's weight on Earth, and her weight on the Moon.

Take the Earth's gravitational field strength as 9.8 N/kg, and the Moon's gravitational field strength as 1.6 N/kg.

Answer:

Step 1: List the known values

Mass, $m = 42 kg$
Gravitational field strength on Earth, $g_{E} = 9.8 N / kg$
Gravitational field strength on Moon, $g_{M} = 1.6 N / kg$

Step 2: State the equation linking weight, mass and gravitational field strength

$g = \frac{W}{m}$

Step 3: Rearrange to make weight the subject

$W = m g$

Step 3: Calculate the weight force exerted on Isabelle on Earth

$W_{E} = m g_{E}$

$W_{E} = 42 \times 9.8$

$W_{E} = 411.6 N = 410 N (2 s . f .)$

Step 4: Calculate the weight force exerted on Isabelle on the Moon

$W_{M} = m g_{M}$

$W_{M} = 42 \times 1.6$

$W_{M} = 67.2 N = 67 N (2 s . f .)$

Step 5: Compare the two values of weight

The weight force is greater on Earth than on the Moon
This is because the Earth has a larger gravitational field strength than the Moon, so Isabelle's weight force is larger on Earth than on the Moon

Exam Tip

You won't be expected the learn the exact value of g (9.81 N/kg), but you will be expected to remember that g = 9.8 N/kg and use it in calculations

Using a balance

The weight of two objects can be compared using a balance
- Because the gravitational field strength is constant everywhere on Earth, this also allows us to measure the mass of an object

$m = \frac{W}{g}$

Types of balance, IGCSE & GCSE Physics revision notes

A balance can be used to compare two different weights

Balances can be digital or analogue
- The object being measured is placed on the balance
- The reading given is mass in kg or g
Force meters or newtonmeters consist of a spring and hook
- The object being measured is hung from the hook
- The reading given is weight in N

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