Analytical studies-toolbox

• Learning Outcomes After the session the you will be 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 Newtonian mechanics

By

Drs J. Whitty and B. Henderson

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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, it scalar quantity.

Velocity on the other hand is a vector because it is defined by magnitude and direction thus: Velocity is the distance moved in a defined direction per unit time.

t

sspeed

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direction specified ain travelleddistance

Force & Motion

Momentum is essentially the quantity of motion, we will see later that all bodies in motion have momentum, defined as the product of mass 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/skg

Conservation of MomentumMomentum cannot be destroyed or created

Consequence??

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

Class Examples

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 in a car of 3 tonne travelling at 6km/h. Calculate the final velocity after the crash.

Further Examples

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 their common 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.

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…..

Sir Isaac Newton

Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, England

Died: 31 March 1727 in London, England

Principia Mathematica

The Greatest Scientific Work Ever Written?

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.

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Third Law: For every action there is an equal and opposite reaction. Class Examples Time

Class Examples

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

A tennis player stuck a ball so that its path is exactly reversed. The ball approached the racket at 35m/s and left at 45m/s. The mass of the ball was 90g. Find the magnitude of the force on the ball if the racket is contact with the ball for 0.25s

Find the breaking force of 20tonne engine travelling at 50kph if the breaks are applied for 3s reducing its speed by 9kph.

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, the force, being known as the inertial force, and the traction resistance due to friction, head wind, etc., this force known as the tractive force

Class Examples Time: Force & Motion Questions

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 a rope 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, calculate the vertical acceleration of the lift.

Further examples: Physics in the class room

Further Questions

1. A body of mass 40kg is acted upon by a resultant force of 90N. Find the acceleration of the body.

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

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

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

b. Find the greatest possible tension in the lift cable if the string must remain in tact and fails at 600N

Connected Particles

Particles of mass 3kg and 5kg area attached to ends of a light in extendable string as shown.

How could we work out the acceleration of the system and hence the tension in the string

3kg 5kg

3kg

5kg

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 drop vertically 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 stings and hence the resulting acceleration of the system.

Summary

Have we met our learning objectives, specifically, are you now 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

If so when and where, were they met!

Examination type question

State Newton’s 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 any assumptions made [4]

2kg 3kg