2.16–2.18Gravity
Weight is the force acting on an object due to gravity. The force of gravity close to the Earth is due to the gravitational field around the Earth.
The weight of an object depends on the gravitational field strength at the point where the object is.
The weight of an object can be calculated using the equation:
weight = mass × gravitational field strength W = m g
weight, W, in newtons, N; mass, m, in kilograms, kg; gravitational field strength, g, in newtons per kilogram, N/kg. In any calculation the value of g will be given.
You should be able to recall and apply this equation.
The weight of an object may be considered to act at a single point, referred to as the object's centre of mass.
The weight of an object and the mass of an object are directly proportional. You should recognise and be able to use the symbol for proportionality, ∝, so this can be written W ∝ m.
Weight is measured using a calibrated spring-balance, a newtonmeter.
Worked example
An astronaut has a mass of 80 kg. Calculate their weight on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg).
- Write the equation: W = m g.
- On Earth: W = 80 × 9.8 = 784 N.
- On the Moon: W = 80 × 1.6 = 128 N.
- Note what has changed and what has not: the mass is 80 kg in both places.
- Only the gravitational field strength differs, so only the weight differs.
Answer: 784 N on Earth and 128 N on the Moon. The mass is unchanged at 80 kg — mass is a scalar property of the object, while weight is a force that depends on where the object is.
Common mistake
Mass is in kilograms and weight is in newtons. Saying an object "weighs 80 kg" is wrong in physics — 80 kg is its mass, and its weight is the force in newtons that gravity exerts on it.
- Weight
- the force acting on an object due to gravity, calculated as mass × gravitational field strength
2.14Forces, accelerations and Newton's Laws of motion
The three laws that follow answer three different questions, and it helps to know which is which before reading them.
• The First Law asks what happens when the resultant force is zero — the answer is that the velocity does not change. • The Second Law asks what happens when it is not zero — the answer is that the object accelerates, and by how much. • The Third Law is not about one object at all. It is about what two interacting objects do to each other.
A question that mentions balanced forces or a steady speed is a First Law question; one that gives you a force and a mass is a Second Law question; one that asks about a pair of objects pushing on each other is a Third Law question.
2.14Newton's First Law
Newton's First Law: if the resultant force acting on an object is zero and:
• the object is stationary, the object remains stationary • the object is moving, the object continues to move at the same speed and in the same direction — so the object continues to move at the same velocity.
So when a vehicle travels at a steady speed the resistive forces balance the driving force. And the velocity — speed and/or direction — of an object will only change if a resultant force is acting on the object.
You should be able to apply Newton's First Law to explain the motion of objects moving with a uniform velocity, and objects where the speed and/or direction changes.
Common mistake
A moving object does not need a resultant force to keep moving. It needs one only to change its velocity. A car at a steady speed has balanced forces, not a forward resultant.
- Newton's First Law
- if the resultant force on an object is zero, a stationary object remains stationary and a moving object continues at the same velocity
2.15, 2.19Newton's Second Law
Newton's Second Law: the acceleration of an object is proportional to the resultant force acting on the object, and inversely proportional to the mass of the object.
You should recognise and be able to use the symbol for proportionality, ∝, so this is a ∝ F and a ∝ 1/m.
As an equation:
resultant force = mass × acceleration F = m a
force, F, in newtons, N; mass, m, in kilograms, kg; acceleration, a, in metres per second squared, m/s².
You should be able to recall and apply this equation.
You should also be able to estimate the speed, accelerations and forces involved in large accelerations for everyday road transport, and recognise and use the symbol that indicates an approximate value or approximate answer, ~.
Worked example
A resultant force of 1300 N acts on a car of mass 1040 kg. Calculate the acceleration.
- Write the equation: F = m a.
- Rearrange for acceleration: a = F ÷ m.
- Substitute: a = 1300 ÷ 1040.
- = 1.25.
- Give the unit: metres per second squared.
Answer: 1.25 m/s²
Required practical 7
Investigate the effect of force and mass on acceleration
- Set a trolley on a runway with a length of string over a pulley at the end, carrying a hanging mass to provide the accelerating force.
- Place two light gates a measured distance apart, connected to a data logger, so the trolley's velocity at each gate can be recorded and the acceleration calculated.
- Compensate for friction by tilting the runway slightly until the trolley moves at a constant speed when given a gentle push with no hanging mass.
- To vary the force: keep the total mass of the system constant by moving masses from the trolley to the hanger, rather than simply adding more to the hanger.
- Record the acceleration for each force, repeating each measurement and taking a mean.
- To vary the mass: keep the hanging mass the same and add masses to the trolley, recording the acceleration each time.
Common mistake
F in F = m a is the resultant force, not the driving force. If a question gives a driving force and a resistive force, subtract them first.
2.22InertiaHigher tier
Higher tier: the tendency of objects to continue in their state of rest or of uniform motion is called inertia.
Inertia is not a force. It is the name for the behaviour the First Law describes — the fact that an object will not change its velocity by itself. It is why a passenger continues forwards when a car brakes sharply, and why a heavy trolley is hard to get moving and, once moving, hard to stop.
- Inertia
- the tendency of an object to continue in its state of rest or of uniform motion
2.22Inertial massHigher tier
Higher tier students should be able to explain that:
• inertial mass is a measure of how difficult it is to change the velocity of an object • inertial mass is defined as the ratio of force over acceleration.
That second point is just the Second Law rearranged: m = F ÷ a. Reading it that way makes the first point obvious — if a large force produces only a small acceleration, the ratio is large, and the object is hard to get moving or to stop.
Worked example
A resultant force of 240 N gives an object an acceleration of 0.60 m/s². Calculate its inertial mass.
- Inertial mass is defined as the ratio of force over acceleration.
- So m = F ÷ a.
- Substitute: m = 240 ÷ 0.60.
- = 400.
- Give the unit: kilograms.
Answer: 400 kg
- Inertial mass
- a measure of how difficult it is to change the velocity of an object, defined as the ratio of force over acceleration
2.23Newton's Third Law
Newton's Third Law: whenever two objects interact, the forces they exert on each other are equal and opposite.
You should be able to apply Newton's Third Law to examples of equilibrium situations.
The crucial detail is that the two forces act on different objects. A book on a table: the book pushes down on the table, and the table pushes up on the book. Those are a Third Law pair. The weight of the book and the table's upward push are not a Third Law pair, even though they are equal and opposite — because both act on the same object, the book.
Common mistake
If two forces act on the same object, they are not a Newton's Third Law pair. A Third Law pair is always the same type of force, acting on two different objects, in opposite directions.
2.20–2.21Motion in a circleHigher tier
Higher tier students should be able to explain qualitatively, with examples, that motion in a circle involves constant speed but changing velocity.
An object going round a circular track at a steady 10 m/s has a constant speed — the number never changes. But its direction is changing continuously, and velocity includes direction, so the velocity is changing all the time. A changing velocity means the object is accelerating, which means there must be a resultant force acting on it, directed towards the centre of the circle. A satellite in orbit and a car on a roundabout are both examples.
Common mistake
Constant speed does not mean constant velocity. Anything moving in a curve has a changing velocity, and therefore an acceleration, even at a steady speed.
Before you practise
- weight = mass × gravitational field strength, in newtons.
- Mass is the same everywhere; weight changes with the field strength.
- First law: with no resultant force an object stays still or keeps a constant velocity.
- Second law: force = mass × acceleration.
- Third law: for every action there is an equal and opposite reaction — the pair act on DIFFERENT objects.
- Inertial mass measures how hard it is to change an object's velocity, and equals force ÷ acceleration.
- In a circle at constant speed the direction changes, so the velocity changes and there must be a centripetal force towards the centre.