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’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 lawIf 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 lawNo matter how long the bowl, this always happens

Newton’s first lawNo matter how long the bowl, this always happens.

constant velocity

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

Newton’s first lawThe 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

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

gravity

Air resistance

Other examples

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

gravity

Air resistance

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

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.

Constant velocity

Pushing force

friction

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 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.

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!

5 m/s1000kg

2000kgBefore

After

V m/s

Combined mass = 3000 kg

Momentum before = 1000x5 + 2000x0 = 5000 kg.m/s

Momentum after = 3000v

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!

10kg

4kg-4.5 m/s7 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

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”)

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.

Constant velocity

Pushing force

friction

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!

Pushing force

friction

acceleration

Remember from last year that acceleration is rate of change of velocity. In other words

acceleration = (change in velocity)/time

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)

Pushing force

friction

Ms Weston’s Porche

Newton’s 2nd law

There is a mathematical relationship between the resultant force and acceleration.

Resultant force (N) = mass (kg) x acceleration (m/s2)

FR = maIt’s physics,

there’s always a mathematical relationship!

An example

What will be Mr Dickens’ acceleration?

Pushing force (100 N)

Friction (60 N)

Mass of Mr Dickens and bike = 100 kg

An example

Resultant force = 100 – 60 = 40 N

FR = ma

40 = 100a

a = 0.4 m/s2

Pushing force (100 N)

Friction (60 N)

Mass of Mr Dickens and bike = 100 kg

Newton’s 3rd lawIf 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

W (weight)

T (tension in rope)

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

Examples

• String over a pulley

T (tension in rope)

T (tension in rope)

W1

W1

Examples

• Ladder leaning against a wall

R

R

F

F

W

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?

10 000 N

?? 10°

Vertically 10 000 = 2 X ? X sin10°

10 000 N

?? 10°

? X sin10° ? X sin10°

Vertically 10 000/2xsin10° = ?

10 000 N

?? 10°

? X sin10° ? X sin10°

? = 28 800 N

10 000 N

?? 10°

? X sin10° ? X sin10°

What happens as the angle deceases?

10 000 N

?? θ? = 10 000/2xsinθ

Let’s try some questions!

Page 67 Question 2Page 68 Questions 6, 8, 10.Page 73 Questions 3, 4, 5

Page 74 Question 9, 12Page 75 Question 14

Page 84 Questions 2, 3, 4, 5, 6, 8, 9

Page 85 Questions 13, 16, 20, 21.