Calculating Weight (AQA GCSE Physics)

• Mass (measured in kilograms, kg) is related to the amount of matter in an object
• Weight (measured in newtons, N) is the force of gravity on a mass
  • The weight of an object and the mass of an object are directly proportional
  • The size of this force depends on the gravitational field strength (often called gravity, g, for short)

• Weight, mass and gravitational field strength are related using the equation:

• g is known as the acceleration due to gravity or the gravitational field strength
• On Earth, this is equal to 9.81 m/s² (or N/kg)

Free Fall

• An object in free fall is falling solely under the influence of gravity
• On Earth, all free-falling objects accelerate towards Earth at a rate of 9.81 m/s²
• In the absence of air resistance, all bodies near the Earth will fall with the same acceleration regardless of their mass

Mass v 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

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

• 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:

Gravitational field strength of the planets in our solar system

Step 1: List the known quantities

• • Weight on Mars, W_M = 190 N
  • Gravitational field strength on Mars, g_M = 3.8 N/kg
  • Gravitational field strength on Earth, g_E = 9.8 N/kg

Step 2: Write out the equation relating mass and weight and rearrange for mass

W = mg

• • Divide both sides by g:

Step 3: Calculate the student’s mass

• • The student’s mass is the same anywhere in the universe

Step 4: Calculate the student’s weight on Earth

W_E = m × g_E = 50 × 9.8 = 490 N