Mass & Weight
Section: Physics | Syllabus: Cambridge IGCSE Combined Science (0653)
Mass
- Mass is a measure of the quantity of matter in an object at rest relative to the observer
- mass does not depend on where the object is
- mass stays the same wherever the object is taken - on Earth, on the Moon, or in space
- Because of this, mass is the property of an object that resists a change in its motion
- the greater an object's mass, the harder it is to speed it up, slow it down, or change its direction
- Mass is a scalar quantity - it has magnitude (size) but no direction
- SI unit:
- kilogram (kg)
Converting grams and kilograms
- Mass is sometimes given in grams (g), but must be converted to kilograms before use in calculations
- Conversion:
- 1000 g = 1 kg
- 1 g = 0.001 kg
- To convert g to kg, divide the mass in g by 1000
- To convert kg to g, multiply the mass in kg by 1000
Question: Museli buys a bag of rice with a mass of 2.75 kg. State the mass of the rice in grams (g).
State the conversion between kg and g. 1 kg = 1000 g AnswerConvert kg into g by multiplying by 1000. m = 2.75 × 1000 m = 2750 g
Weight
- Weight is a gravitational force acting on an object because it has mass
- Since weight is a force, it is a vector quantity - it has both magnitude and direction
- SI unit:
- newton (N)
Examiner Tip
- Mass and weight are often confused because the words are used interchangeably in everyday speech
- in Physics, they mean very different things, and you should be able to explain the difference clearly
- mass is the amount of matter an object has - it is a scalar quantity, measured in kg
- weight is a force - it is a vector quantity, measured in N
Weight and Gravitational Field Strength
- Weight is the effect of a gravitational field on a mass
- Weight is defined as the force acting on an object with mass when it is placed in a gravitational field
- Planets have strong gravitational fields
- so they attract nearby masses with a strong gravitational force
- Because of weight:
- objects stay firmly on the ground
- objects will always fall toward the ground
- satellites are kept in orbit
Diagram showing examples of the weight force in action: an object resting on the ground, an object falling, and a satellite held in orbit by gravitational attraction
Gravitational Field Strength
- Gravitational field strength (g) is defined as the force per unit mass acting on an object in a gravitational field
- Formula:
- g = (W/m)
- Where:
- g = gravitational field strength (N/kg)
- W = weight (N)
- m = mass (kg)
- Near the Earth's surface:
- g ≈ 9.8 N/kg
Gravitational field strength and free fall
- An object in free fall in a vacuum, in a uniform gravitational field, accelerates at a rate also called g
- in this context, g = acceleration of free fall
- near the Earth's surface, g ≈ 9.8 m/s^2
- Gravitational field strength and acceleration of free fall are equivalent quantities
- this is why the same number, 9.8, appears both as N/kg and as m/s²
Examiner Tip
- You won't be expected to learn the exact value of g (9.81 N/kg), but you should remember and use g = 9.8 N/kg in calculations
Mass vs Weight
- An object's mass always remains the same, regardless of its location in the universe
- The weight force exerted on an object depends on the strength of the gravitational field at its location
- for example, the gravitational field strength on the Moon is 1.6 N/kg, meaning an object's weight there is about 6 times less than on Earth
Diagram comparing a person on Earth and on the Moon, showing that mass stays the same in both locations but weight is much lower on the Moon due to its weaker gravitational field
Worked ExampleQuestion: Muchindu is training to be a cosmonaut and has a mass of 58 kg. Compare Muchindu's weight on Earth with their weight on the Moon.
Take the Earth's gravitational field strength as 9.8 N/kg, and the Moon's as 1.6 N/kg Weight on Earth: W = mg = 58 × 9.8 = 568.4 N Weight on Moon: W = mg = 58 × 1.6 = 92.8 N AnswerMuchindu weighs 568.4 N on Earth but only 92.8 N on the Moon — about 6 times less, since the Moon's gravitational field strength is about 6 times smaller than Earth's
- Step 1: List the known values
- mass, m = 58 kg
- gravitational field strength on Earth, g_E = 9.8 N/kg
- gravitational field strength on Moon, g_M = 1.6 N/kg
- Step 2: State the equation linking weight, mass, and gravitational field strength
- g = (W/m)
- Step 3: Rearrange to make weight the subject
- W = mg
- Step 4: Calculate Muchindu's weight on Earth
- W_E = m g_E = 58 × 9.8
- W_E = 568.4 N ≈ 570 N (2 s.f.)
- Step 5: Calculate Muchindu's weight on the Moon
- W_M = m g_M = 58 × 1.6
- W_M = 92.8 N ≈ 93 N (2 s.f.)
- Step 6: Compare the two values
- the weight force is greater on Earth than on the Moon
- this is because Earth has a larger gravitational field strength than the Moon, so Muchindu's weight is larger on Earth
Comparing Mass and Weight Using a Balance
- The weight of two objects can be compared using a balance
- Because gravitational field strength is constant everywhere on Earth, a balance can also be used to measure mass
- m = (W/g)
- Balances can be digital or analogue:
- the object being measured is placed on the balance
- the reading given is mass, in kg or g
- Force meters, or newton meters, consist of a spring and a hook:
- the object being measured is hung from the hook
- the reading given is weight, in N
Question: Muumbe hangs a rock from a newton meter and reads a weight of 7.84 N. Calculate the mass of the rock. Take g = 9.8 N/kg.
State the equation linking mass, weight, and gravitational field strength. m = (W/g) AnswerSubstitute the known values. m = (7.84/9.8) m = 0.8 kg
Diagram comparing a beam or digital balance used to measure mass in kg, and a spring balance (newton meter) used to measure weight in N
Mass vs Weight - Summary
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