Mass & Weight (Cambridge (CIE) IGCSE Physics): Revision Note

Mass & weight

Mass

• Mass is defined as:

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

• 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 kg 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)

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

Defining gravitational field strength

• Gravitational field strength is defined as:

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

• Near to the surface of the Earth, this is approximately 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 $g$

  • 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

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

Using a balance

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

  • Because the gravitational field strength is approximately constant everywhere on Earth, this also allows us to measure the mass of an object

 $m=\frac{W}{g}$

• 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 newton meters, consist of a spring and hook

  • The object being measured is hung from the hook

  • The reading given is weight in N