CIE A Level Physics: Momentum and Newton's Laws of Motion

Mass

Mass is a measure of the amount of matter in an object.

Weight

Weight is the effect of a gravitational field on a mass.

SI unit for mass

The SI unit for mass is the kilogram (kg).

Weight formula

The weight of a body is equal to the product of its mass and the acceleration of free fall: W = mg.

Acceleration of free fall on Earth

The acceleration of free fall, g, on Earth, is 9.81 m s−2.

Gravitational field strength

Gravitational field strength (in N kg−1) and acceleration due to free fall (in m s−2) are just two ways of describing the same thing.

Free fall

An object in free fall is falling solely under the influence of gravitational attraction.

Mass vs Weight

An object's mass always remains the same; however, its weight will differ depending on the strength of the gravitational field at different locations.

Gravitational field strength on the Moon

The gravitational field strength on the Moon is 1.63 N kg−1.

Acceleration due to gravity on the Moon

The acceleration due to gravity on the Moon is 1/6 of that on Earth.

Newton's second law of motion

Newton's second law of motion tells us that objects will accelerate if there is a resultant force acting upon them.

Force formula

F = ma, where F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m s−2).

Resultant force

The resultant force is the vector sum of all the forces acting on the body.

Acceleration direction

Acceleration can be either positive or negative depending on the direction of the resultant force.

Positive acceleration

An object will speed up (positive acceleration) if the resultant force acts in the same direction as the direction of motion.

Negative acceleration

An object will slow down (negative acceleration) if the resultant force acts in the opposite direction to the direction of motion.

Rocket thrust example

A rocket produces an upward thrust of 15 MN and has a weight of 8 MN.

Air resistance example

When in flight, the force due to air resistance is 500 kN.

Resultant force calculation

The resultant force acting on the rocket is F = 15×10^6 N - 8×10^6 N - 500×10^3 N = 6.5×10^6 N upwards.

Mass of the rocket

The mass of the rocket is 0.8 × 10^6 kg.

Acceleration calculation

The acceleration of the rocket is a = F/m = 6.5×10^6 N / 0.8×10^6 kg = 81 m s−2.

Direction of acceleration

The direction of the acceleration is upwards.

Examiner Tip on direction

You can choose which direction is positive as long as you are consistent throughout your calculation.

Linear momentum

Linear momentum, p, is defined as the product of mass and velocity.

Momentum formula

p = mv

Units of linear momentum

p = linear momentum in kilogram metres per second (kg m s⁻¹)

Mass unit

m = mass in kilograms (kg)

Velocity unit

v = velocity in metres per second (m s⁻¹)

Vector quantity

Momentum is a vector quantity; it has both magnitude and direction.

Positive momentum

If an object travelling to the right has positive momentum, an object travelling to the left has a negative momentum.

Negative momentum

When the ball is travelling in the opposite direction, its velocity is negative, and its momentum is also negative.

Tennis ball mass

Mass of tennis ball, mT = 0.06 kg

Tennis ball velocity

Velocity of tennis ball, vT = 75 m s⁻¹

Brick mass

Mass of brick, mB = 3 kg

Brick velocity

Velocity of brick, vB = 1.5 m s⁻¹

Tennis ball momentum

pT = mT × vT = 0.06 × 75 = 4.5 kg m s⁻¹

Brick momentum

pB = mB × vB = 3 × 1.5 = 4.5 kg m s⁻¹

Force definition

Force is defined as the rate of change of momentum.

Change in momentum

Change in momentum, Δp, can also be expressed as: Δp = pfinal − pinitial.

Initial momentum

pi = m × vi = 1500 × 15 = 22,500 kg m s⁻¹

Final momentum

pf = m × vf = 1500 × (−5) = −7,500 kg m s⁻¹

Change in momentum calculation

Δp = pf − pi = −7500 − 22500 = −30,000 kg m s⁻¹

Average force calculation

F = Δp / Δt = −30,000 / 3 = −10,000 N

Newton's third law

The force exerted by the wall on the car will be equal in magnitude and opposite in direction to the force exerted by the car on the wall.

Impact force relationship

The force exerted is also determined by the time taken for the impact to occur.

Force and time relationship

As Δt increases, F decreases, when Δp remains the same.

First ball force

F = Δp / Δt1 = 0.5 / 2.0 = 0.25 N

Second ball force

F = Δp / Δt2 = 0.5 / 0.1 = 5.0 N

Greatest force

The second tennis ball exerted the greatest force on the racket.

Newton's First Law of Motion

A body will remain at rest or move with constant velocity unless acted on by a resultant force.

Equilibrium

If the forces acting on an object are balanced, the object is said to be in equilibrium.

Resultant Force

There is no resultant force (the resultant force = 0) when the forces are balanced.

Change in Motion

If the forces acting on an object are not balanced, there is a resultant force and a change in the object's motion.

Acceleration

The object may speed up (acceleration) when acted upon by a resultant force.

Negative Acceleration

The object may slow down (negative acceleration) when acted upon by a resultant force.

Change in Direction

The object may change direction (a change in velocity, hence acceleration) when acted upon by a resultant force.

Driving Force

The driving force exerted by the engine on the car is 6 kN.

Frictional Forces

The magnitude of the frictional forces acting on the car is equal to the driving force, which is 6 kN.

Newton's Second Law of Motion

A resultant force acting on a body will cause a change in the object's motion in the direction of the force.

Rate of Change in Momentum

The rate of change in momentum is proportional to the magnitude of the force.

Newton's Second Law Equation

F = ma, where F = force in newtons (N), m = mass in kilograms (kg), a = acceleration in metres per second squared (m s^-2).

Acceleration Equation

a = ∆v / ∆t, where ∆v is the change in velocity and ∆t is the change in time.

Combined Mass Calculation

The combined mass of the girl and the skateboard is calculated to be 60 kg.

Newton's Third Law of Motion

Whenever two bodies interact, the forces they exert on each other are equal and opposite.

Force Interaction

If body A exerts a force on body B, then body B will exert a force on body A of equal magnitude but in the opposite direction.

Newton's Third Law Force Pair

A Newton's third law force pair must be the same type of force, the same magnitude, opposite in direction, and acting on different objects.

Free-body Force Diagram

A free-body force diagram illustrates the forces acting on an object.

Balanced Forces

The book is at rest because the two forces acting on it are balanced - i.e. there is no resultant force.

Criteria for Newton's Third Law

Just because you see two forces in opposite directions doesn't mean they are a Newton's third law force pairs; specific criteria must be met.

Misleading Definition of Third Law

Avoid using the definition 'For every action is an equal and opposite reaction' as it can be misleading.