Weight & Mass
Mass
- Mass is defined as
The amount of matter in an object
- The standard 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
Worked example
An object has a mass of 2.7 kg.
State the number of grams in 2.7 kg.
Answer:
Step 1: State the conversion between g and kg
- 1 kg = 1000 g
Step 2: Convert 2.7 kg into g
2.7 kg = 2.7 × 1000 = 2700 g
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 10 N/kg
- So, an object of mass 1 kg weights 10 N
- 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
Weight
- Weight is a gravitational force on an object with mass
- The standard SI units for force are newtons (N)
- Weight is the effect of a gravitational field on a mass
- Weight is defined as:
The force of gravity acting on an object
- Because of weight:
- Objects stay firmly on the ground
- Objects will always fall to the ground
- Satellites are kept in orbit
- Weight can be calculated using the equation:
W = mg
- Where:
- W = weight (N)
- m = mass (kg)
- g = gravitational field strength (N/kg)
Weight vs Mass
- An object’s mass always remains the same, however, its weight will differ depending on the strength of the gravitational field on the planet or stellar object it is on or near
- 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
Comparing your Weight on Earth and the Moon
On the moon, your mass will stay the same but your weight will be much lower due to the smaller 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 40 kg.
Comment on the difference between Isabelle's weight on Earth, and her weight on the Moon.
Take the Earth's gravitational field strength as 10 N/kg, and the Moon's gravitational field strength as 2 N/kg.
Answer:
Step 1: State the equation linking weight and mass
-
- The equation linking weight and mass is:
W = m × g
Step 2: List the known values
-
- The question instructs us to take the Earth's gravitational field strength as 10 N/kg
- The question also instructs us to take the Moon's gravitational field strength as 2 N/kg
- Mass, m = 40 kg
Step 3: Calculate Isabelle's weight on Earth
-
- Substituting the values of mass and Earth's gravitational field strength into the equation gives:
W = 40 × 10 = 400 N
Step 4: Calculate Isabelle's weight on the Moon
-
- Substituting the values of mass and the Moon's gravitational field strength into the equation gives:
W = 40 × 2 = 80 N
Step 5: Comment on the two values of weight
-
- Isabelle's weight 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 (the force of gravity pulling down on her) is larger on Earth than on the Moon
Exam Tip
It is a common misconception that mass and weight are the same, but they are very different. An objects mass is the same no matter where it is in the universe. An object's weight changes depending on where it is within a gravitational field. Your mass is the same on Earth and the Moon but is different on Earth and the Moon.
Higher-tier students can rearrange the weight equation with the help of the formula triangle:
The Formula Triangle For the Weight Equation
Use the formula triangle to help you rearrange the equation
