# 5.1.5 Calculating Weight

### Mass v Weight

• 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)

#### Exam Tip

It is a common misconception that mass and weight are the same, but they are in fact very different

• Since weight is a force – it is a vector quantity
• Since mass is an amount – it is a scalar quantity

### Calculating Weight

• 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

#### Worked Example

A student estimates they would have a weight of 190 N on Mars.

The gravitational field strength on Earth is 9.8 N/kg. The gravitational field strength on Mars is 3.8 N/kg.

Calculate the weight of the student on Earth.

Step 1: List the known quantities

• Weight on Mars, WM = 190 N
• Gravitational field strength on Mars, gM = 3.8 N/kg
• Gravitational field strength on Earth, gE = 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

WE = m × gE = 50 × 9.8 = 490 N

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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