9.3 - conservation of momentum

what is newton’s third law?

• when two objects interact, they exert equal and opposite forces on each other

• every action has a reaction

which one of newton’s laws state that when two objects interact, they exert equal and opposite forces on each other?

newton’s third law

what are the forces at play for an object on earth according to newton’s third law?

the earth exerts a force due to gravity on an object which exerts an equal and opposite force on the earth

what are the forces at play for a jet engine according to newton’s third law?

• jet engine exerts a force on hot gas in the engine to expel the gas

• the gas being expelled exerts an equal and opposite force on the engine

what is a force pair?

two forces of the same type and acting on different objects

why isn’t a plant pot on a table considered a force pair?

idk

maybe some questions about whats constituting as a force pair

what are two forces of the same type acting on different objects?

a force pair

what is required to change the momentum of an object?

resultant force

what happens when an object has a resultant force?

it gains momentum

can an object have momentum if it doesn’t have a resultant force?

no

what does the principle of conservation of momentum state?

for a system of interacting objects, the total momentum remains constant, provided no external resultant force acts on the system

for a system of interacting objects, the total momentum remains constant, provided no external resultant force acts on the system - what is this?

the principle of conservation of momentum

when does the principle of conservation of momentum no longer applicable?

when an external resultant force acts on the system

according to the principle of conservation of momentum, what is the total momentum?

constant (providing no external resultant force acts on the system)

why is the total momentum (providing no external resultant force acts on the system) unchanged according to the principle of conservation of momentum?

as the objects in the system exert equal and opposite forces on each other when in contact, the change of the momentum of one object is equal and opposite to the change of momentum of the other object

how is momentum transferred?

via interactions between objects

what is the momentum for two objects that collide, then separate?

• the momentum of each object changes

• as the objects exert equal and opposite forces on each other when in contact, the change of the momentum of one object is equal and opposite to the change of momentum of the other object

• i.e., the momentum loss from one object = the momentum gain of the other

what are the forces at play when two objects collide and then separate?

• they exert equal and opposite forces only when they are in contact

• the objects are force pairs

for two objects colliding then separating, when are the forces exerted between them equal and opposite?

when they’re in contact

for two objects colliding then separating, are they force pairs?

yes

for two objects colliding then separating, why are they force pairs?

because they are of the same type and act on different objects

what is the total final momentum in a collision?

total final momentum = total initial momentum

why is the total final momentum unchanged in a collision?

derivation here with the balls

questions on the ball thing

what is the velocity of colliding objects that stick together after colliding?

they have the same velocity

what is the equation for momentum of two objects that stick together after colliding?

(m_B + m_A) V = m_A u_A

name values here

(m_B + m_A) V = m_A u_A

momentum of two objects that stick together after colliding

derive (m_B + m_A) V = m_A u_A

here

how can we test conservation of moment?

• by using a motion sensor linked to a computer

• using light gates linked to a computer or data logger

what is the apparatus for the experiment testing conservation of momentum?

here

what happens in the experiment testing conservation of momentum?

1. the mass of each trolley is measured before the test

2. with trolley B at rest, trolley A is pushed so it moves towards B at constant velocity

3. the two trolleys stick together on impact

4. the computer records and displays the velocity of A throughout this time

in the experiment testing conservation of momentum, what is the point of the computer?

to display the velocity of trolley A throughout the collision time

how does the experiment testing conservation of momentum prove momentum is conserved?

• the computer display shows that the velocity of A dropped suddenly when the impact took place

• the velocity of A immediately before (u_A) and after (v_a) the collision can be measured. the measurements should show that the total momentum of both trolleys is equal to the momentum of trolley A before the collision, i.e., (m_B + m_A) V = m_A u_A

in the experiment testing conservation of momentum, what is happening at the point the computer display drops?

the impact point

in the experiment testing conservation of momentum, where is the impact point on the computer display?

the point where the computer display drops

(m_B + m_A) V = m_A u_A

this is for the experiment but idk if its the general equation for conservation of momentum

what is the equation for (m_B + m_A) V = m_A u_A this thing idk what it is

(m_B + m_A) V = m_A u_A

wait for me…

derive (m_B + m_A) V = m_A u_A

in a sec

how can we test the conservation of momentum using light gates?

1. light gates linked to a computer or a data logger

2. card attached to A passes through the first of two light gates

3. B is positioned so that A collides with it just after passing through the first light gate

4. u_A = card length / time taken to pass through first gate

5. v_a = card length / time taken to pass through second gate

here

what is the apparatus for testing conservation of momentum using light gates?

here

in a head on collision, what is needed to completely stop the colliding objects after the impact?

total final momentum to be zero, which could only happen if the initial momentum of one object was exactly equal and opposite to that of the other object

in a head on collision, what is needed for the total final momentum to be zero?

for the initial momentum of one object was exactly equal and opposite to that of the other object

what happens to the momentum in a head on collision, considering the colliding objects don’t come to a complete stop?

there is a total resultant momentum, either positive or negative according to the direction