Transcript Speed & Velocity

Analytical studies-toolbox
Introduction to Newtonian
mechanics
By
Drs J. Whitty and B. Henderson
• 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
Ft  mv1  mv2
F  ma
Speed & Velocity
Speed is defined as distance travel in a predefined
direction, s, per unit time, t.
distance travelled
s
speed 

time taken
t
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.
distance travelled in a specified direction
s
speed 

time taken
t
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:
momentum  mass  velocity  mv
All bodies are in motion have momentum. The unit
for momentum is kgm/s . Since it is the product
of mass (kg) and velocity (m/s).
Conservation of Momentum
Momentum cannot be destroyed or created
Consequence??
The Consequence of to
Conservation of Momentum
1.
2.
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?
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.
2.
3.
4.
Evaluate the momentum of a 2T car travelling at
30km/h.
A particle of 12kg is travelling with a momentum of
100kgm/s, calculate its velocity.
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.
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.
2.
3.
4.
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
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
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
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.
Ft  mv1  mv2
F  ma
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 applications
Consider 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 motion
The 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.
2.
3.
4.
A mass of 60kg is suspended on the end of a rope.
Determine the tension in the rope.
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.
Determine the tension in a rope supporting a mass
of 35kg if it is moving at 3m/s2.
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.
b.
Find the tension in the string if the lift
accelerates at a rate of 1.2m/s/s
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)
b)
evaluate the acceleration of
the following connected
system. [10]
Explain which laws of motion
are in place and any
assumptions made [4]
2kg
3kg