Resonance Curves of Multidimensional Chaotic Systems

1
Last week Collision means the action of bodies
striking or coming together (touching). Collision
s involve forces which cause is a sudden change
in velocity. Collisions can be elastic, meaning
they conserve energy, inelastic, meaning they do
not conserve not energy, or totally inelastic (or
plastic), meaning the object stick together.
2

• Work
• Context Do a work out. Carrying a chair
  upstairs.
• Definition Work displacement force
• Discussion
• Work work done by a force on an object
• Displacement displacement of the object
• Force component of a force on the object in the
  direction of the displacement

3

• Discussion of work
• Lifting a 2lbs ball by 2ft Work 4lbs-ft
• Lifting a 3kg object by 2m Work (weight force)
  isplacement (3kg9.8m/s2) 2m 58.8
  kg-m/s2 58.8 Joule
• Lowering a 3kg object by 2m Work (weight
  force) displacement (3kg9.8m/s2) (-2m)
  -58.8 kg-m/s2 -58.8 Joule
• Joule is the unit of work
• Pulling a heavy, but frictionless cart Work
  zero
• Pulling a cart with a force of 2Newton
  Work2Newtondistance

4

• Simple Machine An Incline
• Context Humans can not produce large
• forces, but they can apply a small force
• for a long period of time.
• Definition An incline is a ramp for lifting
• heavy objects to a given height.
• Discussion
  An incline
• Force Weight height / (length of ramp)
• Small slope ? long ramp ? small force
• Work Force (length of ramp) Weight height
• Example Lifting a 100lbs object by 1ft over a
  10ft ramp ?force 10lbs
• 1097 Forces and Work on Ramp

5
Simple Machine A Lever Context Work in Work
out. The work we do on the lever is equal to
the work the lever does on the object.
A lever
Lect. Demo Pliers,
Hydraulic Jack Definition A lever (from French
lever, "to raise", c.f. a levant) is a rigid
object that is used with an appropriate fulcrum
or pivot point to multiply the mechanical force
that can be applied to another object. A lever
has a long and a short arm. The short arm creates
large forces but moves short distances. (Short
arm force)(Short arm distance) (Long arm
force)(Long arm distance)
Work in
Work out
6
Simple Machine A Pulley Context Lifting heavy
objects without a ramp.
A pulley

Definition A pulley (also called a sheave or
block) is a wheel with a groove between two
flanges around its circumference. The groove
normally locates a rope, cable or belt. Pulleys
are used to change the direction of an applied
force, or realize a mechanical advantage
. Weightlift (pulling force)(distance
pulled) Work out Work in Distance pulled
lift (number of strings) Pulling force
weight / (number of strings) mechanical
advantage!
7

• Work Energy Theorem
• Context Newton second law
• describes the effect of a force
• on the motion of an object
• force mass acceleration.
• What is the relation between
• force and speed.
• 
  Illustration of Work-Energy Theorem
• Definition
• - If the total work done on some object by all
  forces is positive, the object speeds up.
• If the total work done on some object by all
  forces is negative, the object slows down.

8

• Work
• Definition Work displacement force
• Work work done by a force on an object
• Displacement displacement of the object
• Force component of a force on the object in the
  direction of the displacement