P2.2.2 Momentum

P2 Physics

KS4 ADDITIONAL SCIENCEMr D Powell

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Connection

• Connect your learning to the content of the lesson

• Share the process by which the learning will actually take place

• Explore the outcomes of the learning, emphasising why this will be beneficial for the learner

Demonstration

• Use formative feedback – Assessment for Learning

• Vary the groupings within the classroom for the purpose of learning – individual; pair; group/team; friendship; teacher selected; single sex; mixed sex

• Offer different ways for the students to demonstrate their understanding

• Allow the students to “show off” their learning

Activation

• Construct problem-solving challenges for the students

• Use a multi-sensory approach – VAK• Promote a language of learning to

enable the students to talk about their progress or obstacles to it

• Learning as an active process, so the students aren’t passive receptors

Consolidation

• Structure active reflection on the lesson content and the process of learning

• Seek transfer between “subjects”• Review the learning from this lesson and

preview the learning for the next• Promote ways in which the students will

remember• A “news broadcast” approach to learning

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P2.2.2 Momentuma) Momentum is a property of moving objects.

p = m x v

b) In a closed system the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum.

p is momentum in kilograms metres per second, kg m/sm is the mass in kilograms, kgv is the velocity in metres per second, m/s

Candidates may be required to complete calculations involving two objects. Examples of events are collisions and explosions.

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Practical / Demo

Suggested ideas for practical/demonstrations to develop skills and understanding include the following:

investigating the transfer of Ep to Ek by dropping a card through a light gate.

plan and carry out an investigation to measure velocity using trolleys and ramps.

running upstairs and calculating work done and power, lifting weights to measure power.

a motor lifting a load to show how power changes with load.

stretching different materials before using as catapults to show the different amounts of energy transferred, indicated by speed reached by the object or distance travelled.

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Momentum Defined AMomentum is important to anyone who plays a contact sport. In a game of rugby, a player with a lot of momentum is very difficult to stop.

The momentum of a moving object = its mass x velocity.

momentum = mv

The unit of momentum is the kilogram meter/second (kg m/s).

a) Calculate the momentum of a 40 kg person running at 6 m/s.b) Calculate the momentum of a 80 kg person running at 3 m/s.c) Calculate the velocity of a 80 kg bike with momentum of 2kg m/s.d) Calculate the mass of a person with momentum of 2kg m/s and

velocity of 0.02 m/s

a) 240kg m/sb) 240kg m/sc) 0.025m/sd) 100kg

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Investigating Momentum Simply... AUsing only your fingers, a few similar coins, the desk, a stopclock and ruler can you explore the concept of momentum and come up with any rules of thumb or prove the formulae.

The momentum of a moving object = its mass x velocityp = mv

You could investigate?

Distance of travelMass movedFlick strengthTime of travelAverage Speed /Velocity1. Pick a variable to keep the same

2. Pick a variable to change3. Make a table4. Record your results5. Make a comment

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Results

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

Distance Travelled in m

Number of 2p Coins

Dis

tanc

e Tr

avel

led

in m

Number of Coins

Distance Travelled in m

1 0.452 0.243 0.164 0.145 0.09

These results broadly show that if we double the mass of the object the distance travelled by the object for the same flick halves.

Hence if we doubled the flick force each time we doubled the mass it would make sense that the coin would then move as far each time!

Why not think in terms of flick as the intital velocity u

Hence:

p = mu or p = mass x flick speed

Momentum changes as mass changes…..

A

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Mars LandersAnother interesting idea about momentum is looking at the change in momentum during a collision.

When you stop suddenly (i.e. land on mars) your velocity changes quickly and there is an initial and final velocity. Also a force on you and a time that it happens it. The formulae for this is;

You are going to explore this idea by making a Mars lander for a fresh egg. The idea is to make the force on the egg as little as possible over the crash as you drop it from as high as possible. If you kill egg your pilot is dead!

You have 25 minutes to design your craft & your equipment is;

1 x egg8 x A4 paper1 x 3m strip of sticky tape3 x human brains per team

t

mumvF

v=final velu = initial velt = timeF = force

A

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Comparing Momentum

We can also easily see that an object with;

more mass more velocity more mass and velocity

Will have a larger momentum;

momentum = mass x velocity

25m/s

1000kg

50m/s

1000kg

10m/s

6000kg

30m/s6000kg

25,000 kg m/s

50,000 kg m/s

180,000 kg m/s

60,000 kg m/s

1

2

3

4

D

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Investigating Collisions AWhen two objects collide, the momentum of each object changes.;

A. Trolley A is given a push so it collides with a stationary trolley B.

B. The two trolleys stick together after the collision. (bluetac)

C. The computer gives the velocity of A before the collision and the velocity of both trolleys afterwards.

1. What does each section of the velocity–time graph show?

2. Why does the velocity reduce?

3. Can you come up with any written formulae from what you know about momentum to describe the change?

1. Before and after the collision

2. The mass of trolley B absorbs some of the KE of trolley A

3. mAvA + mBvB = mABvAB

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Investigating Collisions AIn fact we can use the generic formulae;

mAvA + mBvB = mABvAB

To describe any change in momentum for this type of collision. Also you may see the trucks called Number 1 & 2

1. For two trolleys of the same mass, the velocity of trolley A is halved by the impact. The combined mass after the collision is twice the moving mass before the collision. So the momentum (mass x velocity) after the collision is the same as before the collision.

2. For a single trolley pushed into a double trolley, the velocity of A is reduced to one-third. The combined mass after the collision is three times the initial mass. So once again, momentum after the collision is the same as the momentum before the collision.

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Worked Example.. TASK: Read this information here ( stick the print out in your book) Can you do your own worked example which is similar....

A

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Car shunts... A

If a vehicle crashes into the back of a line of cars, each car in turn is ‘shunted’into the one in front. Momentum is transferred along the line of cars to the oneat the front.

1. If you have ever been in one of these or seen one of these where does the energy eventually go?

2. What do you think that we must assume when completing simple calculations on momentum in the exam?

mAvA + mBvB = mABvAB

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Summary Questions... D

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Can you see the link... (there are two) A

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Momentum

If we are considering mass and velocity we can combine them into a more useful form which describes both at the same time and allows comparisons between events and objects.

We can say that

momentum = mass x velocity

It is also important to realise that velocity is a directional quantity so it can be negative or positive.

30m/s

- 30m/s

A

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Bounces

When these trucks bounce off each other we consider that all the momentum is transferred to the blue truck

Crashes / Collision

When these trucks connect to each other we consider that the momentum is shared between blue truck & red truck

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Explosions... AIn explosion trolley examples:

momentum of A after = mAvA

momentum of B after = mBvB

total momentum before = 0 (because both trolleys were at rest).

Using conservation of momentum gives:

mAvA + mBvB = 0Or rearange;

mAvA = -mBvB

This tells us that A and B move apart with equal and opposite amounts ofMomentum and the idea of velocity being a vector is shown!

TASK: Read this information then write a note entitled “What is an explosion” (in terms of momentum)

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Explosions in guns... DWhen a shell is fired from an artillery gun, the gun barrel recoils backwards.

The recoil of the gun barrel is slowed down by a spring. This lessens the backwards motion of the gun. An artillery gun of mass 2000 kg fires a shell of mass 20 kg at a velocity of 120m/s. Calculate the recoil velocity of the gun? mAvA = -mBvB

TASK: Write down this example (in brief) for your book & calculate the velocity.....

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Plenary Question... CA 600kg cannon recoils at a speed of 0.5m/s when a 12kg cannon ball is fired from it.

1. Write out the formulae you will use.

2. Rearrange to calculate the velocity of the cannon ball when it leaves the cannon.

3. Make sure you include a unit in your answer

mAvA = -mBvB

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Summary Questions C

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Which word links all of these images... S

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Impacts.... A

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Force & Momentum

Sub in for “a”

F=ma&(v-u)/t = a

A

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What does it mean?

The equation shows that:

Making the time longer (increasing the value of t) makes the force smaller. Crumple zones in cars are designed to make impact times longer so impact forces are reduced.

When a resultant force acts on a moving object, a change of momentumtakes place. In general, the force needed to cause a change of momentum is given by:

A

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Example..... DScientists at Oxford University have developed new lightweight material for bullet-proof vests.

The material is so strong and elastic that bullets bounce off it. A bullet of mass 0.004 kg moving at a velocity of 90 m/s is stopped by a bulletproof vest in 0.0003 s. What is the impact force?

1. Now try the same calculation but with a time of 0.0002s

2. Now try the same calculation but with a mass of 0.008kg?

3. Now try same calculation but with a velocity of 120m/s

t = 2/3 so F = -1800Nm = x2 so F = -2400Nv = 4/3 so F = -1600N

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Plenary Questions... C

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TASK

You have now watched the horizon movie on crash testing can you write an extended paragraph including your own comments and thoughts on;

What were they trying to do?

What is the Physics of the situation ?

What tests were completed; cadavers, live, animals, dummies.

Why did they test them?

Do you agree or disagree with what was done

What part do the car companies play in the grand scheme of things

What changes have occurred in society in the past 80 years?

t

mumvF

Mr Powell 2012Index

P2.2.2 Momentum

a) Momentum is a property of moving objects.

p = m x v

b) In a closed system the total momentum before an event is equal to the total momentum after the event. This is called “conservation of momentum”.

p is momentum in kilograms metres per second, kg m/sm is the mass in kilograms, kgv is the velocity in metres per second, m/s

Candidates may be required to complete calculations involving two objects.

Examples of events are collisions and explosions.

P2.2.2 Momentum

a) Momentum is a property of moving objects.

p = m x v

b) In a closed system the total momentum before an event is equal to the total momentum after the event. This is called “conservation of momentum”.

p is momentum in kilograms metres per second, kg m/sm is the mass in kilograms, kgv is the velocity in metres per second, m/s

Candidates may be required to complete calculations involving two objects.

Examples of events are collisions and explosions.

P2.2.2 Momentum

a) Momentum is a property of moving objects.

p = m x v

b) In a closed system the total momentum before an event is equal to the total momentum after the event. This is called “conservation of momentum”.

p is momentum in kilograms metres per second, kg m/sm is the mass in kilograms, kgv is the velocity in metres per second, m/s

Candidates may be required to complete calculations involving two objects.

Examples of events are collisions and explosions.