# Newton’s Laws of Motion

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Newton’s Laws of Motion
That’s me!

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

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

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

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

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).

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

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

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

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

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

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

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

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) Air resistance gravity

Oooops!

Another example Imagine Mr Dickens cycling at constant velocity.

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

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

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

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

Momentum

Momentum 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

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

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

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!

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?

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

Momentum before = momentum after
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

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

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

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

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

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

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

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

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

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

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

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

It’s physics, there’s always a mathematical relationship!
Newton’s 2nd law There is a mathematical relationship between the resultant force and acceleration. Resultant force (N) = mass (kg) x acceleration (m/s2) It’s physics, there’s always a mathematical relationship! FR = ma

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

An example Resultant force = 100 – 60 = 40 N FR = ma 40 = 100a
a = 0.4 m/s2 Mass of Mr Dickens and bike = 100 kg Pushing force (100 N) Friction (60 N)

Newton’s 3rd 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)

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.

Free-body diagrams

Free-body diagrams 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.

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

Examples Inclined slope
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 Inclined slope R (normal reaction force) F (friction) W (weight)

Examples String over a pulley T (tension in rope) T (tension in rope)
W1 W1

Examples Ladder leaning against a wall F R R W F

Resolving vectors into components

Resolving vectors into components
It is sometime useful to split vectors into perpendicular components

Resolving vectors into components

A cable car question

Tension in the cables? ? 10° ? N

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

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

? = N ? 10° ? ? X sin10° ? X sin10° N

What happens as the angle deceases?
? = /2xsinθ ? θ ? N

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.