The Laws of Motion

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9/5/2006 PHY 101 Week2 1 The Laws of Motion …or, Newtonian mechanic

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The Laws of Motion. …or, Newtonian mechanics. Newton’s Laws of Motion. The law of inertia . An object in motion remains in motion with constant velocity if the net force on the object is 0. - PowerPoint PPT Presentation

Transcript of The Laws of Motion

Page 1: The Laws of Motion

9/5/2006 PHY 101 Week2 1

The Laws of Motion…or, Newtonian mechanics

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1. The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0.

2. Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma.

3. Action and reaction. For every action there is an equal but opposite reaction.

Newton’s Laws of Motion

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Newton’s second law

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Newton’s second law of motion

F = m a• F = force acting on the moving object, a vector

• m = mass of the moving object

• a = acceleration of the moving object, a vectorIf the force is known, Newton’s second law states how the object (on which the force is acting) accelerates:

mFa

What is “force?”

What is “mass?”

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Force and acceleration are vectors.

A vector has both magnitude and direction.

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Three kinds of acceleration

m slows down

m speeds up

m changes direction

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UNIFORM CIRCULAR MOTION

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Example

The “string tension” is the strength of the force exerted by the string at either end.

Centripetal acceleration(Christian Huygens ,1673)

ra ˆ rv2

rmvT

2

rF ˆr

mv2Therefore, the force on m is

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Analyze free fall including air friction

up) is direction (-

down) is direction (

CFmgF

Fma

air

gravity

The aerodynamic drag force (C) depends on the size, shape and surface roughness; it is about the same for both balls.

mCgaCmgma or

• The gravitational acceleration (g) is independent of mass.• Effect of air is inversely proportional to mass:

heavy --- small effect of airlight --- large effect of air

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Newton’s third law

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Which vehicle exerts a greater force ― the tow truck or the car?

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1. The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0.

2. Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma.

3. Action and reaction. For every action there is an equal but opposite reaction.

Newton’s laws of motion

Action means force.

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force on B due to A

force on A due to B

Newton’s third law

We will see than this is very hard to accept! It is just not common sense. That is why it took a great genius like Newton to figure it out.

Whenever one object exerts a force on another object, the second object exerts an equal but opposite force on the first object.

Forces always occur like this, in pairs.

For every action there is an equal but opposite reaction.

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Example – A collision

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Universal Gravitation --- an example of Newton’s third law

ˆ

ˆ

2221

2

1221

1

nF

nF

rmGm

rmGm

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The Earth pulls the apple down (“action”).

The apple pulls the Earth up (“reaction”).

The two forces are equal (but opposite).

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When does a scientific theory become an accepted fact?

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The truck pulls to the right. According to Newton’s third law, the car pulls to the left with an equal force. So how can they start moving, or accelerate?

A puzzle:

Resolution: Consider each part separately, and don’t forget that other forces are also acting.

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Harold Edgerton’s high speed photograph of Wes Kessler kicking a football.

The force exerted by the ball on the toe (reaction) is equal to the force exerted by the toe on the ball.

Really hard to accept!

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MomentumMomentum, , p = mvp = mv

Total momentum is conserved:Total momentum is conserved:

constant. is

law) (third

21

21

2211

22

11

21

00

pppp

vmvmtvm

tvm

FF

Proof

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The four fundamental forces

• Gravity

• Electromagnetic

• Strong nuclear force •Weak nuclear force

unified by Maxwell’s theory

not really a force, but an interaction that causes certain radioactive decays

comes from QCD, the interaction of quarks and gluons

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FIN

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Newton’s second law and calculus

0

ttva

mFamaF

as

onaccelerati ousInstantane

or

mF

dtdv

differential equation

Isaac Newton invented calculus to solve the equation of motion – to calculate motion for the force that is acting. Generally, calculus is the mathematics that describes continuous change.