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Newton’s Laws of Motion That’s me!

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Newton’s 1 st Law An object continues in uniform motion in a straight line or at rest unless a resultant external force acts

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Newton’s 1 st Law An object continues in uniform motion in a straight line or at rest unless a resultant external force acts Does this make sense?

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Newton’s 1 st law Newton’s first law was actually discovered by Galileo. Newton nicked it!

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Newton’s first law Galileo imagined a marble rolling in a very smooth (i.e. no friction) bowl.

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Newton’s first law If you let go of the ball, it always rolls up the opposite side until it reaches its original height (this actually comes from the conservation of energy).

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Newton’s first law No matter how long the bowl, this always happens

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Newton’s first law No matter how long the bowl, this always happens. constant velocity

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Newton’s first law Galileo imagined an infinitely long bowl where the ball never reaches the other side!

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Newton’s first law The ball travels with constant velocity until its reaches the other side (which it never does!). Galileo realised that this was the natural state of objects when no (resultant ) forces act. constant velocity

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Other examples Imagine a (giant) dog falling from a tall building

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Other examples To start the dog is travelling slowly. The main force on the dog is gravity, with a little air resistance gravity Air resistance

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Other examples As the dog falls faster, the air resistance increases (note that its weight (force of gravity) stays the same) gravity Air resistance

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Other examples Eventually the air resistance grows until it equals the force of gravity. At this time the dog travels with constant velocity (called its terminal velocity) gravity Air resistance

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Oooops!

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Another example Imagine Mr Dickens cycling at constant velocity.

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Newton’s 1 st law He is providing a pushing force. Constant velocity

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Newton’s 1 st law There is an equal and opposite friction force. Constant velocity Pushing force friction

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Inertia A stationary object only starts to move when you apply a resultant force. A moving object keeps moving at a steady speed in a straight line. To change the speed or direction you need to apply another resultant force

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This reluctance to change velocity is called INERTIA The inertia of an object depends on its mass A bigger mass needs a bigger force to overcome its inertia and change in motion

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Momentum

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Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as Momentum (kg.m/s) = Mass (kg) x Velocity (m/s) p = mv

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An easy example A lorry has a mass of 10 000 kg and a velocity of 3 m.s -1. What is its momentum? Momentum = Mass x velocity = 10 000 x 3 = 30 000 kg.m.s -1.

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The Law of conservation of momentum “in an isolated system, momentum remains constant”.

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momentum before = momentum after In other words, in a collision between two objects, momentum is conserved (total momentum stays the same). i.e. Total momentum before the collision = Total momentum after Momentum is not energy!

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A harder example! A car of mass 1000 kg travelling at 5 m/s hits a stationary truck of mass 2000 kg. After the collision they stick together. What is their joint velocity after the collision?

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A harder example! 5 m/s 1000kg 2000kg Before After V m/s Combined mass = 3000 kg Momentum before = 1000x5 + 2000x0 = 5000 kg.m/s Momentum after = 3000v

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A harder example The law of conservation of momentum tells us that momentum before equals momentum after, so Momentum before = momentum after 5000 = 3000v V = 5000/3000 = 1.67 m/s

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Momentum is a vector Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations

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An even harder example! Snoopy (mass 10kg) running at 4.5 m/s jumps onto a skateboard of mass 4 kg travelling in the opposite direction at 7 m/s. What is the velocity of Snoopy and skateboard after Snoopy has jumped on? I love physics

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An even harder example! 10kg 4kg-4.5 m/s 7 m/s Because they are in opposite directions, we make one velocity negative 14kg v m/s Momentum before = 10 x -4.5 + 4 x 7 = -45 + 28 = -17 Momentum after = 14v

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An even harder example! Momentum before = Momentum after -17 = 14v V = -17/14 = -1.21 m/s The negative sign tells us that the velocity is from left to right (we choose this as our “negative direction”)

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Newton’s second law Newton’s second law concerns examples where there is a resultant force. I thought of this law myself!

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Let’s go back to Mr Dickens on his bike. Remember when the forces are balanced (no resultant force) he travels at constant velocity. Constant velocity Pushing force friction

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Newton’s 2nd law Now lets imagine what happens if he pedals faster. Pushing force friction

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Newton’s 2nd law His velocity changes (goes faster). He accelerates! Pushing force friction acceleration Remember from last year that acceleration is rate of change of velocity. In other words acceleration = (change in velocity)/time

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Newton’s 2nd law Now imagine what happens if he stops pedalling. friction

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Newton’s 2nd law He slows down (decelerates). This is a negative acceleration. friction

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Newton’s 2nd law So when there is a resultant force, an object accelerates (changes velocity) Pushing force friction Ms Weston’s Porche

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Newton’s 2 nd law There is a mathematical relationship between the resultant force and acceleration. Resultant force (N) = mass (kg) x acceleration (m/s 2 ) F R = ma It’s physics, there’s always a mathematical relationship!

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An example What will be Mr Dickens’ acceleration? Pushing force (100 N) Friction (60 N) Mass of Mr Dickens and bike = 100 kg

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An example Resultant force = 100 – 60 = 40 N F R = ma 40 = 100a a = 0.4 m/s 2 Pushing force (100 N) Friction (60 N) Mass of Mr Dickens and bike = 100 kg

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Newton’s 3 rd law If a body A exerts a force on body B, body B will exert an equal but opposite force on body A. Hand (body A) exerts force on table (body B) Table (body B) exerts force on hand (body A)

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Forces always act in pairs. So why don’t these forces just cancel out with no effect?? The 2 forces act on different objects so cannot cancel each other out.

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Free-body diagrams

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Shows the magnitude and direction of all forces acting on a single body The diagram shows the body only and the forces acting on it.

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Examples Mass hanging on a rope W (weight) T (tension in rope)

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Examples Inclined slope W (weight) R (normal reaction force) F (friction) If a body touches another body there is a force of reaction or contact force. The force is perpendicular to the body exerting the force

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Examples String over a pulley T (tension in rope) W1W1 W1W1

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Examples Ladder leaning against a wall R R F F W

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Resolving vectors into components

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It is sometime useful to split vectors into perpendicular components

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Resolving vectors into components

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A cable car question

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Tension in the cables? 10 000 N ? ? 10°

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Vertically 10 000 = 2 X ? X sin10° 10 000 N ? ? 10° ? X sin10°

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Vertically 10 000/2xsin10° = ? 10 000 N ? ? 10° ? X sin10°

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? = 28 800 N 10 000 N ? ? 10° ? X sin10°

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What happens as the angle deceases? 10 000 N ? ? θ ? = 10 000/2 x sinθ

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Let’s try some questions! Page 67 Question 2 Page 68 Questions 6, 8, 10. Page 73 Questions 3, 4, 5 Page 74 Question 9, 12 Page 75 Question 14 Page 84 Questions 2, 3, 4, 5, 6, 8, 9 Page 85 Questions 13, 16, 20, 21.

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