Weight, mass and gravitational field strengthIB MYP Physics: Revision notes
Section 1
Mass and weight are different
Mass is the amount of matter in an object. It is measured in kilograms (kg), is a scalar and does not change with location.
Weight is the force of gravity acting on an object. It is measured in newtons (N), is a force and changes with the strength of gravity.
An astronaut has the same mass on Earth and on the Moon, but a much smaller weight on the Moon.
Do not say 'my weight is 50 kg'. Mass is in kg; weight is a force in N.
Section 2
The equation W = mg
Weight = mass × gravitational field strength, or W = m g.
Worked example: a 4 kg bag on Earth (g = 10 N/kg) has weight W = 4 × 10 = 40 N. On the Moon (g = 1.6 N/kg) the same bag weighs 4 × 1.6 = 6.4 N.
Rearranged, g = W ÷ m, which is why g is measured in newtons per kilogram.
Section 3
Gravitational field strength in different places
Gravitational field strength (g) is the force of gravity on each kilogram of mass.
- Earth: 10 N/kg (more precisely about 9.8 N/kg)
- Moon: about 1.6 N/kg
- Jupiter: about 25 N/kg, which is larger than Earth because Jupiter is far more massive
The bigger the planet's mass, the greater its field strength at the surface.
Section 4
Gravitational fields
A gravitational field is a region where a mass feels a force because of gravity. Every object with mass has a gravitational field, but only large objects such as planets create fields strong enough to notice.
The field pulls masses towards the centre of the planet, so the force of gravity acts downwards on everything near the surface.
Section 5
Measuring weight
Weight is measured with a newton meter (spring balance). Hang the object from the hook and read the scale when it hangs still. The spring stretches more for a larger force.
To find mass from weight, use m = W ÷ g.
Worked example: a newton meter reads 12 N on Earth. The mass is 12 ÷ 10 = 1.2 kg.
A newton meter measures weight, so on the Moon the same object gives a smaller reading. A balance that compares masses gives the same result everywhere.
Must Know
- Mass (kg) is the amount of matter and never changes
- Weight (N) is the force of gravity: W = mg
- g ≈ 10 N/kg on Earth, about 1.6 N/kg on the Moon, about 25 N/kg on Jupiter
- A gravitational field is a region where masses feel a force
- Weight is measured with a newton meter
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Weight, mass and gravitational field strength
- An astronaut of mass 60 kg is training for a mission to the Moon. The gravitational field strength is 10 N/kg on Earth and 1.6 N/kg on the Moon.Explain why the astronaut's mass is the same on the Moon, but her weight is different.2 marks
- A space probe carries a standard mass of 2.0 kg on a newton meter to measure the gravitational field strength at different places. On Earth the newton meter reads 20 N. Near Jupiter it reads 50 N.Describe how a newton meter is used to find the weight of the standard mass.2 marks
- A group of students investigates the relationship between mass and weight on Earth. They hang masses of 0.1, 0.2, 0.3, 0.4 and 0.5 kg from a newton meter. The readings are 1.0, 2.0, 3.1, 4.0 and 5.0 N.Describe the trend in the results and calculate the value of weight ÷ mass for the 0.4 kg mass.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).