9.1 - momentum + impulse

what does the effect of a collision depend on?

the colliding bodies’ initial velocities and mass

who discovered momentum?

newton

what is momentum?

• the momentum of a moving object is its mass x its velocity, (p = m v)

• the effect a force has on an object’s movement

p = m v

momentum of a moving object

what is the equation for the momentum of a moving object?

p = m v

• p = momentum of the moving object

• m = object mass

• v = object velocity

which has momentum - a still object or a moving one?

moving object

what doesn’t have momentum - a still object or a moving one?

still object

why does a moving object have momentum but a still object doesn’t?

momentum relates to the effect a force has on an object’s movement, so a still object would not have any momentum as its not moving

how did newton discover momentum?

• he realised a force was needed to change the velocity of an object

• he realised that the effect of a force on an object depended on its mass as well as the amount of force

when does momentum apply?

in the motion of objects of almost any situations apart from;

• inside the atom

• in strong gravitational fields

• at speeds approaching the speed of light

when doesn’t momentum apply?

• inside the atom

• in strong gravitational fields

• at speeds approaching the speed of light

what affects the motion of an object in almost all situations?

momentum

what affects the motion of an object in the atom?

the rules of quantum physics

what affects the motion of an object in strong gravitational fields?

einsten’s theory or relativity

what affects the motion of objects at speeds approaching the speed of light?

einstein’s theory of relativity

for which object motion does einstein’s theory of relativity affect?

• object’s in strong gravitational fields

• object’s moving at speeds nearing the speed of light

for which object motion do the rules of quantum physics affect?

situations inside the atom

why doesn’t momentum apply to situations inside the atom?

because the rules of quantum physics apply instead

why doesn’t momentum apply at speeds nearing the speed of light?

because einstein’s theory of relatively applies instead

why doesn’t momentum apply for objects in strong gravitational fields?

because einstein’s theory of relatively applies instead

what is the launch of a rocket planned according to?

• newton’s laws of motion (i.e., momentum)

• newton’s law of gravitation

what did newton’s theory of momentum go on to discover?

newton’s laws of motion

what do we use to predict the existence of black holes?

einstein’s rules of general relativity

what happens when the gravitational field an object is in is weak?

einstein’s theory of relatively can simplify into newton’s laws

what happens when an object moves at speeds much lower than the speed of light?

einstein’s theory of relatively can simplify into newton’s laws

what can simplify into newton’s laws of motion - the rules of quantum physics or newton’s laws of relativity?

newton’s laws of relativity

what can’t simplify into newton’s laws of motion - the rules of quantum physics or newton’s laws of relativity?

the rules of quantum physics

why can newton’s laws of relativity simplify into the laws of motion, but the rules of quantum physics cannot?

because movement due to the laws of relativity is conditional (e.g., affected by speed and position), but a sub-atomic particle is always subatomic

when does einstein’s theory of relatively simplify to newton’s laws of motion?

• when the gravitational force acting on an object is weak

• when an object is moving at speeds much less than the speed of light

what is the unit for momentum?

• kilograms per metre (kg m s^-1)

• newton seconds (N s)

N s

unit of measurement for momentum

kg m s^-1

unit of measurement for momentum

what is the symbol for momentum?

p

is momentum a vector or scalar quantity?

vector

why is momentum a vector quantity?

it has a magnitude and direction

what is the direction of momentum?

in the same direction as the object’s velocity

is the direction of momentum the same / different to the direction of object velocity?

same direction

what does an object’s velocity act in the same direction as?

the object’s momentum

newton’s first law of motion

an object remains at rest or in uniform motion unless acted on by a force

an object remains at rest or in uniform motion unless acted on by a force

newton’s first law of motion

newton’s second law of motion

the resultant force acting on an object at constant mass is proportional to the object’s acceleration, (F = m a)

the resultant force acting on an object at constant mass is proportional to the object’s acceleration, (F = m a)

newton’s second law of motion

newton’s third law of motion

for every action, there is an equal and opposite reaction

for every action, there is an equal and opposite reaction

newton’s third law of motion

what does newton’s first law tell us about momentum?

what is needed to change the velocity of an object?

a force is needed

what is needed to change the momentum of an object?

a force

why is a force needed to change the velocity of an object?

bcuz, according to newton’s first law, an object will remain at rest or in uniform motion unless acted on by a force

why is a force needed to change the momentum of an object?

• newton’s first law states an object will remain at rest or in uniform motion unless acted on by a force

• so when a force acts on an object, the object’s velocity changes

• p = m v

• as mass is constant, an object’s momentum varies with varying speed from the applied force

which of newton’s laws of motion tell us a force is needed to change the velocity of an object?

newton’s first law - an object remains at rest or in uniform motion unless acted on by a force

which of newton’s laws of motion tell us a force is needed to change the momentum of an object?

newton’s first law - an object remains at rest or in uniform motion unless acted on by a force

when is the momentum of an object constant?

when there is no resultant force acting on the object and mass is constant

what is the momentum of an object when there is no resultant force acting on it?

constant (considering the mass is constant)

what is the velocity of an object when there is no resultant force acting on it?

constant (according to newton’s first law)

what is the velocity of an object when momentum and mass are constant?

constant

why is the velocity of an object constant when momentum and mass are constant?

bcuz momentum can’t be constant if velocity and mass aren’t constant

what happens when an object with constant momentum gains / losses mass?

object velocity changes

why does the object velocity change when an object with constant momentum gains / losses mass?

p = m v, so velocity must compensate for changing mass to keep momentum constant

for an object with constant momentum, what happens to velocity when the object gains mass?

velocity decreases

for an object with constant momentum, what happens to velocity when the object losses mass?

velocity increases

for an object with constant momentum, what happens to mass when the object speeds up?

object loses mass

for an object with constant momentum, what happens to mass when the object slows down?

object gains mass

for an object with constant mass, what happens to momentum when the object speeds up?

momentum increases

for an object with constant mass, what happens to momentum when the object slows down?

momentum decreases

F ∝ ?

F ∝ [m (v - u)] / t

• change of momentum per second

• F = force applied

• m = constant mass of an object

• v = final velocity

• u = initial velocity

• t = time taken for speed to increase from u to v

F ∝ [m (v - u)] / t

force applied to an object of constant mass is proportional to the change of momentum per second

derive F ∝ [m (v - u)] / t

1. newton’s second law states F = m a

2. if a constant forces acts on an object of constant mass, it will accelerate from speed u to speed v

3. initial momentum = m u

   final momentum = m v

   change in momentum = m v - m u

4. newton’s second law states force is proportional to the change of momentum per sec

5. therefore F ∝ change in momentum / time taken

   = [m v - m u] / t

   = [m (v - u)] / t

6. = m a, where a = (v - u) / t

what is force proportional to?

• mass x acceleration

• change in momentum

why does newton’s second law state force is proportional to change in momentum?

• newton’s law states F ∝ mass x acceleration

• acceleration = (v - u) / t

• the equation for change in momentum is F ∝ [m (v - u)] / t

• (v - u) / t can be replaced for a

• therefore newton’s second law states force is proportional to change in motion

a = (v - u) / t

acceleration of an object

derive F = m a

• newton’s second law states F ∝ m a

• F ∝ m a can be rewritten as F = k m a, where k is a constant of proportionality

• value of k is made equal to one by defining the unit of force, newton, as the amount of force that gives an object of mass 1 kg an acceleration of 1 ms^-2

• so F = 1 x m a

• therefore F = m a

what is a newton?

• unit of force

• the amount of force that gives an object of mass 1 kg an acceleration of 1 ms^-2

• the constant of proportionality for a F = m a

how much force is in a newton?

the amount of force needed to give an object of mass 1 kg an acceleration of 1 ms^-2

why is a newton defined the way it is?

• newton’s second law states F ∝ m a

• F ∝ m a can be rewritten as F = k m a, where k is a constant of proportionality

• value of k is made equal to one by defining the unit of force, newton, as the amount of force that gives an object of mass 1 kg an acceleration of 1 ms^-2

• so F = 1 x m a

• therefore F = m a

what is the unit for change in momentum?

Δ (m v)

Δ (m v)

change in momentum

for an object of changing momentum, F = ?

F = Δ (m v) / Δ t

F = Δ (m v) / Δ t

force applied to an object of changing momentum

what is the change of momentum when mass is constant?

m Δ v

m Δ v

change in momentum when mass is constant

for an object of changing momentum and constant mass, F = ?

F = (m Δ v) / Δ t

F = (m Δ v) / Δ t

force applied to an object of changing momentum and constant mass

when does F = Δ (m v) / Δ t apply?

it always applies

when does F = m a apply?

only to objects of constant mass

which always applies - F = Δ (m v) / Δ t or F = m a?

F = Δ (m v) / Δ t

which only applies to objects of constant mass - F = Δ (m v) / Δ t or F = m a?

F = m a

why does F = m a only apply to objects of constant mass?

it is newton’s second law, which is for constant mass. if mass were changing then there would be a change in momentum, so F = Δ (m v) / Δ t would have to be used

for an object where mass changes at a constant rate due to mass being transferred at a constant velocity, F = ?

F = (v Δ m) / Δ t

F = (v Δ m) / Δ t

force of an object where mass changes at a constant rate due to mass being transferred at a constant velocity

what would cause mass to change at a constant rate in an object?

mass being transferred at a constant velocity

derive F = (v Δ m) / Δ t

• F = m a

• change of mass per second = Δ m / Δ t

• therefore F = (v Δ m) / Δ t

what are examples of mass changing at a constant rate?

a rocket ejecting burnt fuel as hot gas from its engine at a constant speed

for an object of changing mass at a constant rate, what is the force for?

the force exerted by the engine to gain / lose the mass

when are these force equations used? -

F = m a

F = Δ (m v) / Δ t

F = (m Δ v) / Δ t

F = (v Δ m) / Δ t

F Δ t = Δ (m v)

F t = m v - m u

F = m a : newton’s second law for constant mass

F = Δ (m v) / Δ t : for changing momentum in a given time

F = (m Δ v) / Δ t : for constant mass and changing velocity

F = (v Δ m) / Δ t : for constant velocity and changing mass

F Δ t = Δ (m v) : impulse

F t = m (v - u) : for constant mass and constant force, i.e., changing velocity

what are the forces at play for a rocket ejecting burnt fuel?

• force exerted by engine to eject burnt fuel as hot gas = F = (v Δ m) / Δ t

• an equal and opposite reaction force acts on the jet engine due to the hot gas, propelling the rocket forwards

why will a rocket continue to move forwards even when ejecting burnt fuel from its engine?

an equal and opposite reaction force acts on the jet engine due to the hot gas, propelling the rocket forwards

what is the impulse?

• force x time for which the force acts

• F Δ t = Δ (m v)

• = change of momentum of the object

what is the symbol for impulse?

F Δ t or Δ (m v)

F Δ t = Δ (m v)

impulse of a force

what is the impulse of a force equal to?

the change in momentum of the object, Δ (m v)