Engineering 1h Lecturer: Bill Easson

1
Engineering 1hLecturer Bill Easson

• Dynamics Module
• (Also known as Mech Eng)
• http//www.see.ed.ac.uk/bille

2
Administrative Details

• Duration
• Lectures 12 hours Tutorials 3 hours
• Times
• LecturesMonday 10.00 - 11.00 LT4 Appleton Tower
• Tutorials
• See Engineering 1h course guide and notice board
• Lecturer
• Professor Bill Easson Room 132, Sanderson
  Building, KB. tel [phone] email
  Bill.Easson_at_ed.ac.uk
• Assessment
• See Engineering 1h Course Guide.

3
Aim

• This course aims to provide an introduction to
  Mechanical Engineering. It will give the student
  an insight into the way in which Mechanical
  Engineers approach and analyse problems in
  Mechanics.

4
Learning Outcomes (1)

• By the end of the course, students should be able
  to
• apply Newtons laws to problems involving linear
  motion of single bodies
• apply Newtons laws to problems involving systems
  of connected bodies
• apply Newtons laws to solve problems involving
  uniform circular motion
• understand the need for real, centrally-acting
  forces in circular motion

5
Learning Outcomes (2)

• By the end of the course, students should be able
  to
• identify situations where the principles of
  conservation of momentum and/or energy may be
  applied
• use conservation of momentum and/or energy to
  solve simple linear motion problems in dynamics
• solve simple problems in fluid statics
• use Bernoullis equation to analyse simple flows
• use momentum considerations to determine forces
  acting due to jets of fluid

6
You

• Lecture Notes
• You are expected to take your own notes from the
  blackboard / OHP during the lectures as
  necessary.
• Tutorials
• Tutorial sheets and solutions are available from
  my web page. You should attempt tutorial
  questions as the material is covered in the
  course, and attend all tutorials.
• Textbooks
• A textbook is not required for this course. Use
  of the library is, of course, strongly
  recommended!
• Assumed Knowledge
• Higher Maths or equivalent

7
Newtons Laws

• Sir Isaac Newton (1642-1729)
• Principia 1687
• Formulated three laws on which all conventional
  motion is based

8
Newton I

• A particle remains at rest or continues to move
  at a constant speed in a straight line unless
  there is a constant force acting on it
• The most important law
• The one that most people dont understand
• The only one that doesnt have an equation

9
Newton II

• The resultant force on a particle is equal to the
  rate of change of momentum of the particle

The form Fma is only valid if the mass is
constant. This is especially important when
dealing with fluid flows
10
Newton III

• The forces of action and reaction between
  interacting bodies are equal in magnitude and
  opposite in direction

• The force of the Earth on the Sun has the same
  magnitude as the force of the sun on the earth
• The force of a tennis ball on a racket has the
  same magnitude as the force of the racket on the
  ball

11
Adding Forces

• Newtons Laws deal with force, velocity and
  momentum - all vectors
• These are 3D in the real world, but we will deal
  with only 1D or 2D in this course

12
Vector addition
These three forces act together on the particle.
Their effect is equivalent to a single force
which is the vector sum of the forces.
F1
FT is the resultant of the forces F1, F2 and F3
F2
FT
F3
FTF1F2F3
13
Resolving forces (1)

• Forces can be broken down into any number of
  component forces
• It is often convenient to choose two
  perpendicular directions for resolution

F FxFy
14
Resolving forces (2)
FxF cos ? FyF sin ? ?tan-1(Fy/Fx)
If the components are perpendicular, they may be
added independently
FTF1F2F3
FTxF1xF2xF3x
FTyF1yF2yF3y
15
Free body diagrams (1)

• FBD is an essential step in the solution of all
  problems involving forces on bodies
• it is a diagram of the external surface of the
  body - not interested in internal forces
• all other bodies in contact with the one we are
  interested in are replaced by vectors

16
Free body diagrams (2)
mg
R1
R2
Sketch of person standing
Fma R1R2-mgma, but no acceleration
so, R1R2mg
17
Free body diagrams (3)
sketch
free body diagram
18
Free body diagrams (4)

• Rules
• clear sketches
• draw in the correct orientation
• show all forces acting on the body
• dont show any internal forces between different
  parts of the body
• show the forces not the components