Momentum & collisions

Principia Mathematica (1687) 1 Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. 2 The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. 3 To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. Does ‘mtion’ mean ‘velocity’ or ‘momentum’? See Law II... 2

Teaching challenges Newton’s laws of motion are mostly counter-intuitive. Newton himself struggled for many years to produce the consistent account given in Principia. Newton’s 3rd law: students have difficulty identifying force pairs. This is not helped by popular shorthand phrases for Newton 3 (e.g. ‘every action has an equal and opposite reaction’) which do not make clear what the forces are acting on.

Example: a book on a table What forces are acting? Let the book fall – is Newton’s 3rd law broken?

the Earth pulls on the book the book pulls on the Earth Interaction = a forces pair The book and the Earth interact via the force of gravity the Earth pulls on the book and the book pulls on the Earth 5

Forces always come in pairs Newton’s 3rd law All forces arise from an interaction between 2 objects. Identify 3rd law pair of forces, which match the descriptors: same kind of force same magnitude, but opposite direction act on two different objects ‘Visualizing Newton’s 3rd Law’ (YouTube clip) Participants in pairs work on diagnostic questions, and try 3 PP experiments: Action and reaction: trolleys Action and reaction with a metre rule Skateboard forces

Newton said “To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Newton’s examples “Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other.” ...Newton’s examples add immeasurably to the axiomatic statement preceding. 8

Interaction pairs In small groups: Work out what the interaction pair is, in each of these situations: a book resting on a table a car tyre pushing back on the road a foot pushing back on a path a deflating balloon pushing back on air a springy toy pushing down on the table (as the toy launches itself) 9

Getting going C21activity Get a move on C21 video Starting to move C21 activity Getting going

Force – time graphs It is unusual for the force to be constant during an interaction. But in all cases the area under the graph represents the impulse of the force.

Hooke’s law force of the mass pulling on the spring = force of the spring pulling on the mass

Not falling through the floor A sound floor always exerts exactly the right upward force to support a person (or object). Why?

Collisions Elastic collisions - e.g. using Newton’s cradles A moving mass hits a mass that is initially stationary. When the two masses are equal, what happens is … the first one stops, the second one moves off with the same velocity When the moving mass hits a smaller mass … they both move off going forwards When the moving mass hits a larger mass … the moving mass rebounds and the bigger mass moves forwards Think extremes – elephants and ping pong balls! 14

Newton’s 2nd law Impulse = change in momentum expressed in its most general form delta) means ‘change in’ mv is ‘momentum’, a vector (unit is kg m s-1) Ft is the ‘impulse of the force’, a vector (unit is N s) Impulse = change in momentum TASK C21 activity 4.16 Note that units N s = kg m s-1. Ask participants to do C21 Activity AP4.16 Momentum, in pairs.

Momentum is ‘conserved’ Trucks A & B collide. Newton’s 3rd law says The time of interaction (t) is the same for both trucks, so change in momentum of truck A = - change in momentum of truck B In symbols,

Elastic & inelastic collisions Momentum is conserved in ALL interactions. A further test Is kinetic energy ( ) also conserved? Demonstration experiment from www.practicalphysics.org “Explaining elastic and inelastic collisions”. Kinetic energy is only conserved in elastic collisions. Refer back to demo mixing ethanol and water: volume, like KE, is not always conserved.

Class experiments Arrange the runway so that it is friction-compensated. Investigate what happens when: 1 trolley collides with stationary trolley of equal mass 1 trolley collides with 2 stationary trolleys In small groups (3 or 4). Half the groups study elastic collisions, other half study inelastic collisions. Everyone collects ticker tapes to analyse. Calculate the total momentum before and after the collision. In plenary, discuss: 1) any problems with the practicalities (using ticker time, any differences between types of ticker time, friction-compensating); 2) the process of analysing from ticker tapes (units); 3) do these experiments show (within reasonable %) that momentum is conserved? that kinetic energy is conserved in elastic collisions?; and, 4) would you have your pupils do these experiments?

Explosion! single trolley, with spring plunger two trolleys Making pop-corn: What makes the pop-corn jump?

Rocket principle A rocket pushes back on its exhaust gases. The exhaust gases push forward on the rocket. Both forces act for the same time. Force x time experienced by the rocket and its exhaust gases is the same, but in opposite directions. This called the impulse of the force. Force x time = mass x acceleration x time = mass x change in velocity This means that the change of momentum is the same for rocket and its exhaust gases. So the total change in momentum here is zero. Photo: NASA 20

Newton’s 2nd law, again Constant mass: Constant velocity (e.g. rocket): Rocket principle demonstrated with an inflated balloon attached to a wire.

Momentum is conserved The total momentum of a ‘closed system’ (i.e. unaffected by any external forces) does not change, in any interaction. applies at all length scales, from sub-atomic particles to galaxies

Quantitative problems involving momentum

Unifications in physics

Support, references talkphysics.org David Sang (ed., 2011) Teaching secondary physics ASE / Hodder Practical Physics experiments and guidance notes, Topic Forces & motion, Collections Newton’s third law and Collisions