Newton’s Laws of Motion That’s me!. Newton’s 1 st Law An object continues in uniform motion in...
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Transcript of Newton’s Laws of Motion That’s me!. Newton’s 1 st Law An object continues in uniform motion in...
![Page 1: Newton’s Laws of Motion That’s me!. Newton’s 1 st Law An object continues in uniform motion in a straight line or at rest unless a resultant external.](https://reader035.fdocuments.in/reader035/viewer/2022062511/551bdd1a550346b4588b5b9d/html5/thumbnails/1.jpg)
Newton’s Laws of Motion
That’s me!
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Newton’s 1st 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 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?
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Newton’s 1st 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 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).
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Newton’s first lawNo matter how long the bowl, this always happens
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Newton’s first lawNo matter how long the bowl, this always happens.
constant velocity
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Newton’s first lawGalileo imagined an infinitely long bowl where the ball never reaches the other side!
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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
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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 1st law
He is providing a pushing force.
Constant velocity
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Newton’s 1st 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
• 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/s1000kg
2000kgBefore
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/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
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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 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!
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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
FR = ma
40 = 100a
a = 0.4 m/s2
Pushing force (100 N)
Friction (60 N)
Mass of Mr Dickens and bike = 100 kg
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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)
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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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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.
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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)
T (tension in rope)
W1
W1
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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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Resolving vectors into components
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° ? X sin10°
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Vertically 10 000/2xsin10° = ?
10 000 N
?? 10°
? X sin10° ? X sin10°
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? = 28 800 N
10 000 N
?? 10°
? X sin10° ? X sin10°
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What happens as the angle deceases?
10 000 N
?? θ? = 10 000/2xsinθ
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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.