To understand Newton’s Laws and Momentum

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Newton’s First Law of Motion We know that a resultant force is necessary for an object to accelerate. Without a resultant force, it will not change direction or speed Newton’s First Law of Motion An object will remain at rest, or continue to move in a straight line at a constant velocity unless acted upon by a resultant force

Newton’s Third Law When two objects interact, they exert equal and opposite forces on each other. Both forces are of the same type The forces must be acting in opposite directions and on different objects Eg forces on a swimmer

What examples can you think of? Book on table Sitting on stool Car on road Satellite in orbit around the world What are the Newton pairs involved?

Copy table and complete for 2 more examples… Situation Body A Body B Type of force Satellite in orbit around the Earth Satellite Earth Gravitational Book on the table Book Table Push (contact forces) What do you notice happens if you remove one of the forces? The other force vanishes!

A bit of a puzzler to wake you up… This question is adapted from the book ‘Thinking Physics is Gedanken Physics’ by Lewis Carroll Epstein and is one of the most well known physics puzzles. If the force on the carriage due to the horse is equal and opposite to the force on the horse due to the carriage, how can the horse pull the carriage? Is the answer: (a) The horse cannot pull the carriage because the carriage pulls as hard on the horse as the horse pulls on the carriage. (b) The carriage moves because the horse pulls slightly harder on the carriage. (c) The horse pulls the carriage before it has time to react. (d) The horse can pull the carriage only if the horse is heavier than the carriage. (e) Another explanation. What might it be?

The answer is… 1 e) Think about the horizontal forces on the horse. It pushes backwards on the ground with its hooves and there is an equal and opposite force of the ground on the horse, forwards. This must be greater than the backward force of the carriage on the horse, and so the horse accelerates forward. Now think about the horizontal forces on the carriage. The force due to the horse acts on it forwards. Provided this is bigger than any backward frictional force, the carriage will also accelerate forwards.

But… Which law tells us why the carriage and horse travel at a constant velocity once they are moving?

Homework Complete sheet Newton’s Laws and Momentum to revise GCSE work – you may have to look up some of the definitions to remind yourself!

Have a go at this one… 2. A builder’s crane is a simple device that allows a person to haul himself/herself up using a pulley. The builder has a mass of 75 kg and the cradle a mass of 35 kg. The builder pulls on the rope with a force of 650 N. The rope exerts a force of 650 N upwards on the man and 650 N upwards on the cradle. (a) Show that the net upward force on the man is: 650 N + force exerted by the floor of the lift (F) – weight of man (b) Show that the net upward force on the cradle is: 650N – weight of the lift – force man exerts on the cradle (F) The net force in (a) is equal to mass of man x acceleration of man. The net force in (b) is equal to the mass of the cradle x acceleration of the cradle. Both man and cradle have the same acceleration. (c) Calculate the acceleration of the cradle and the force exerted by the man on the floor of the cradle. To do this, you will have to treat the two equations given in (a) and (b) as simultaneous equations.

The answer is… 2 A pair of forces acts at the point of contact between the man and the floor. Label this R, upwards on man, downwards on floor. (a) There are three forces acting on the man: rope force 650 N upwards, force of floor R upwards, weight 75g downwards Resultant upward force on man = 650 + R – 75g (b) There are three forces acting on the cradle: rope force 650 N upwards, force of man on floor R downwards, weight 35g downwards Resultant upward force on cradle = 650 – R – 35g (c) Both man and cradle have acceleration a, so we can write Resultant upward force on cradle = 35a Resultant upward force on man = 75a Now the equations from (a) and (b) become: 75a = 650 + R – 75g 35a = 650 – R – 35g Adding these simultaneous equations eliminates R. This gives: 110a = 1300 – 110g Substituting g = 9.8 m s-2 gives a = 2.0 m s-2 and R = 235 N.

Newton’s Second Law The net (resultant) force acting on an object is directly proportional to the rate of change of its momentum and is in the same direction With Newton’s second law we deal with a resultant force that causes an acceleration to occur. F=ma is a special case of Newton’s second law, which we will cover later…

Linear Momentum Momentum = mass x velocity [𝜌=𝑚 𝑥 𝑣] Units are kgms-1 or Ns Momentum is a vector quantity P rabbit = 5 x 12 = 60 kgms-1 p asteroid = 5x1014 x 100,000 = 5 x 1019kgms-1 p whale = 1.5 x 1015 x 6 = 9 x 1015 kgms-1 p asteroid = 5x1014 x 100,000 = 5 x 1019kgms-1 p whale = 1.5 x 1015 x 6 = 9 x 1015 kgms-1 p rabbit = 5 x 12 = 60 kgms-1 m = 5kg v= 12ms-1 m = 5x1014kg v= 100,000ms-1 m = 1.5x105kg v= 6ms-1

Key definition: Principle of conservation of momentum States that: For a closed system of interacting objects, the total momentum in a specific direction remains constant, as long as no external forces act on the system. (i.e. the total momentum before an interaction will equal the total momentum after the interaction.) m1u1 + m2u2 = m1v1 + m2v2

Example A rugby player or mass 90kg is moving at 8ms-1. He launches a tackle on another player who is stationary and who has a mass of 65kg. Find the total momentum before the collision Find the total momentum after the collision Find the velocity of the two players after the collision Mv = 90x8 = 720Ns, mv= 65x0=0, total momentum before = 720Ns Total momentum after = 720Ns Momentum before = momentum after, 720 = 155 x v (155 kg is combined mass), v=4.65ms-1

Air track collision demo How can we use the air track to verify conservation of momentum?

Elastic and Inelastic Collisions Type of Collision Momentum Total Energy Total Kinetic Energy Perfectly elastic Conserved Inelastic Not conserved

Conservation of momentum Complete the questions on the sheet.

Homework Questions on Inelastic and elastic collisions (complete on sheet and hand in next lesson please)