Calculating Weight & Potential Energy
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)
- 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 10 N/kg (or m/s2)
Gravitational Potential Energy
- 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 10 m/s2
- In the absence of air resistance, all bodies near the Earth will fall with the same acceleration regardless of their mass
- The gravitational potential energy (GPE) of an object is defined as:
The energy an object has due to its height in a gravitational field
- This means:
- If an object is lifted up it will gain GPE
- If it falls, it will lose GPE
- The GPE of an object can be calculated using the equation:
GPE = m × g × h
- Where:
- GPE = gravitational potential energy, in Joules (J)
- m = mass, in kilograms (kg)
- g = gravitational field strength, in Newtons per kilogram (N/kg)
- h = height in metres (m)
Worked example
The acceleration due to gravity on the moon is 1/6 of that on Earth. If the weight of a space probe on the moon is 491 N, calculate its mass.
Worked example
A man of mass 70 kg climbs a flight of stairs that is 3 m higher than the floor. Gravitational field strength is approximately 10 N/kg.
Calculate the increase in his gravitational potential energy store.
Step 1: List the known quantities
-
- Mass of the man, m = 70 kg
- Gravitational field strength, g = 10 N/kg
- Height, h = 3 m
Step 2: Write down the equation for gravitational potential energy
GPE = mgh
Step 3: Calculate the gravitational potential energy
GPE = 70 × 10 × 3 = 2100 J
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.
Step 1: List the known quantities
-
- Gravitational field strength on Earth = 10 N/kg
- Gravitational field strength on the Moon = 2 N/kg
- Mass of Isabelle, m = 40 kg
Step 2: State the equation linking weight and mass
-
- The equation linking weight and mass is:
W = m × g
Step 3: Calculate Isabelle's weight on Earth
-
- Substituting the values of mass and Earth's gravitational field strength into the equation gives:
W (Earth) = 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 (Moon) = 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
Examiner Tip
Read questions about mass and weight carefully, they are not the same!
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
