Mass & Weight (Cambridge O Level Physics)

• Mass is a measure of the quantity of matter in an object at rest relative to the observer
  • Mass is a scalar quantity
  • The SI unit for mass is the kilogram (kg)

• 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
• A mass may sometimes be given in grams (g)
  • 1000 g = 1 kg
  • 1 g = 0.001 kg

• Weight is a gravitational force on an object with mass
  • Weight is a force, so it is a vector quantity
  • The SI units for force are newtons (N)

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

The force acting on an object due to gravitational attraction

• 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

Gravitational forces around Earth

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

• The weight of a body is equal to the product of its mass (m) and the acceleration of free fall (g)

 

$W = mg$

• Where:
  • W = weight (N)
  • m = mass (kg)
  • g = gravitational field strength (m/s² or N/kg)

• You can rearrange this equation with the help of the formula triangle:

Weight equation triangle

Weight, mass and gravitational field strength equation triangle

 

• 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 

• Gravitational field strength is also known as acceleration of free fall, or acceleration due to gravity
  • In this context the units are m/s²

• The value of g (gravitational field strength) varies from planet to planet depending on their mass and radius
• A few examples of varying gravitational field strength are shown below:

g on other planets

Gravitational field strength of the planets in our solar system

Mass vs. Weight

• An object’s mass always remains the same, however, its weight will differ depending on the strength of the gravitational field on different planets
• 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 on the Earth and Moon

On the moon, your mass will stay the same but your weight will be much lower

• 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

 $m = \frac{W}{g}$

Using a balance

A balance can be used to compare two different weights