Analytical science - Newtons mechanics

7/27/2019 Analytical science - Newtons mechanics

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Analytical studies-toolbox

Learning Outcomes

After the session the you willbe able to:

Define and evaluate Speed and Velocity

Define and evaluate Force and Motion

Utilize The Laws of Motion

Apply simple rules of Gravitation

Evaluate the Weight of an object

Introduction to Newtonianmechanics

By

Drs J. Whitty and B. Henderson

maF

mvmvFt

21


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Speed & Velocity

Speed is defined as distance travel in a predefined

direction,s, per unit time, t.

t

sspeed

takentime

travelleddistance

The unit of speed is the meter per second (m/s). Because

speed has magnitude only, itscalarquantity.

Velocity on the other hand is a vectorbecause it is

defined by magnitude and direction thus: Velocity is

the distance moved in a defined direction per unit time.

t

sspeed

takentime

directionspecifiedaintravelleddistance


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Force & Motion

Momentum is essentially the quantity of motion, we will see

later that all bodies in motion have momentum, defined as the

product ofmass and velocity:

mvvelocitymassmomentum

All bodies are in motion have momentum. The unit

for momentum is . Since it is the product

of mass ( ) and velocity (m/s).

kgm/s

kg

Conservation of Momentum

Momentum cannotbe destroyed orcreated

Consequence??


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The Consequence of to

Conservation of Momentum

1. Two particles of identical mass travel at the same

velocity collide and come to rest; what can be said

about their velocities/momentum AND why?

2. A rail truck of 4t is travelling at 4m/s, collides with

another truck of 2t travelling in the opposite

direction at 5m/s. After the collision the trucks

become coupled together. Can the new common

velocity be found?

Class Examples Time


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ClassExamples

1. Evaluate the momentum of a 2T car travelling at

30km/h.

2. A particle of 12kg is travelling with a momentum of

100kgm/s, calculate its velocity.3. A milling operation has an effective mass of 400kg

determine the momentum of the table and the

component with a cutting speed of 200mm/min.

4. A truck of 20 tonne travelling at 50km/h crashes ina car of 3 tonne travelling at 6km/h. Calculate the

final velocity after the crash.


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FurtherExamples

1. A bullet of 45g is fired with a velocity of 600m/s into a freely

suspended 5kg target. Find the common speed of the bullet and the

block

2. Two particles A and B have respective masses of 2kg and 3kg. The

speed of A is twice that of B which is travelling at 2m/s. Find theircommon speed after impact assuming the objects coalesce, when:

a) They are travelling in the same direction

b) They are travelling in opposite directions

3. A sledge hammer of mass 6kg, travelling at 20m/s, strikes the top of

a post of mass 2kg without rebounding.

a) Find the common speed of the hammer and speed after impact

4. A 500kg gun is free to move after firing shoot a shell of 5kg a speed

of 200m/s. Find the recoil of the gun.


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Inertia & Motion

All bodies in rest or motion possess inertia.

Inertia is defined as the resistance a stationary or moving

body has to a change in motion. Bodies with large inertia are

difficult to set on motion or to stop once in motion, while for

small bodies with inertia the converse is true.

To overcome the inertia of a body and cause its motion, a

force must be applied. The effects of this force on the motion

of the body are fully described by three beautifully simple

fundamental Laws of Physics. Penned by the arguably the

greatest scientist/engineer ever. Whom we refer to as the

Father of Modern Physics..


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Sir Isaac Newton

Born: 4 Jan 1643 in Woolsthorpe,

Lincolnshire, England

Died: 31 March 1727 in London, England


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Principia Mathematica

The Greatest Scientific WorkEver

Written?


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The Laws of Motion

First Law: A body will remain at rest or in a state of

constant velocity, unless acted upon by a force.

Second Law: The force exerted in a unit of time is

proportional to the change in the quantity of motion(momentum). Which implies that force is

proportional to mass and acceleration.

maFmvmvFt

21

Third Law: For every action there is an equal and

opposite reaction. Class Examples Time


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ClassExamples

An object of mass 4kg is at rest and receives a forceof 280N over 0.1s. With what speed will it commenceto move.

A tennis player stuck a ball so that its path is exactlyreversed. The ball approached the racket at 35m/sand left at 45m/s. The mass of the ball was 90g. Findthe magnitude of the force on the ball if the racket iscontact with the ball for 0.25s

Find the breaking force of 20tonne engine travellingat 50kph if the breaks are applied for 3s reducing itsspeed by 9kph.


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Consequences of the Third Law

Static and Dynamic applicationsConsider the Machine tool in the notes, here the foundation is

exerting an upward force equal in magnitude on the machine.This upward force is known as the reaction (force). The system

is in static equilibrium. Vehicles in motionThe wheeled vehicle is being accelerated by the external force F.

In this case, the reaction is due to the inertia of the vehicle, theforce, being known as the inertial force, and the traction

resistance due to friction, head wind, etc., this force known asthe tractive force

Class Examples Time:Force & Motion Questions


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Force & Motion Questions

1. A mass of 60kg is suspended on the end of a rope.Determine the tension in the rope.

2. If the mass in the previous question is raised be arope with a uniform acceleration of 2m/s/s, find the

tension in the rope.3. Determine the tension in a rope supporting a mass

of 35kg if it is moving at 3m/s2.

4. The tension if an lift cable is 9850 when raising a lift

of total mass 800kg. Neglecting friction, calculatethe vertical acceleration of the lift.

Further examples: Physics in the class room
http://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.html


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Further Questions

1. A body of mass 40kg is acted upon by aresultant force of 90N. Find the accelerationof the body.

2. What is the force required to accelerate abody of 25kg, 2.1m/s2?

3. A object of 40kg is suspended by a stringfrom the ceiling of a lift 200kg

a. Find the tension in the string if the liftaccelerates at a rate of 1.2m/s/s

b. Find the greatest possible tension in the liftcable if the string must remain in tact and

fails at 600N


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Connected Particles

Particles of mass 3kgand 5kg areaattached to ends of a

light in extendablestring as shown.

How could we workout the acceleration of

the system and hencethe tension in thestring

3kg 5kg

3kg

5kg


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Further Class Example

A block of 4kg rests on a smooth horizontal table. A

further block of 9kg is attached by way of an

inextensible string passing over a pulley at one end

of the table. If the larger block is allowed to dropvertically find the acceleration of the system and

hence the tension in the string.

If an further mass 4kg is attached to the other end of

the table evaluate the tension in each of the stingsand hence the resulting acceleration of the system.


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Summary

Have we met our learning objectives,

specifically, are you nowable to:

Define and evaluate Speed and Velocity

Define and evaluate Force and Motion

Utilize The Laws of Motion

Apply simple rules of Gravitation

Evaluate the Weight of an object

If so when and where, were they met!


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Examination type question

State Newtons three laws of

motion. [6]

a) evaluate the acceleration of

the following connected

system. [10]

b) Explain which laws of motion

are in place and anyassumptions made [4]

2kg 3kg

Analytical science - Newtons mechanics

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