Physics of Amusement Parks

1
Physics of Amusement Parks

• Forces and Motion.
• Energy and its conservation.

2
Newtons Laws of Motion

• Newtons Three Laws of Motion are
• The First Law The Law of Interia.
• The Second Law The Force Law.
• The Third Law Action-Reaction Law.

3
Newtons First Law Inertia Law

• The Law of Inertia.
• An object with no force acting on it remains at
  rest or moves with constant velocity in a
  straight line.

4
Newtons Second Law The Force Law

• The Force Law.
• The acceleration of an object is directly
  proportional to the net force on it and inversely
  proportional to its mass.
• Fma

5
Newtons Third Law of Motion

• Action-Reaction Law.
• When one object exerts a force on a second
  object, the second exerts a force on the first
  that is equal in magnitude but opposite in
  direction

6
Principles of Friction

• Friction acts parallel to the surfaces that are
  in contact and the direction opposite to the
  motion of the object or to the net force tending
  to produce such motion.
• Friction depends on the nature of the materials
  in contact and the smoothness of their surfaces.

7
Principles of Friction

• Sliding friction is usually less than starting
  friction.
• Friction is practically independent of the area
  of contact.
• Starting or sliding friction is directly
  proportional to the force pressing the two
  surfaces together.

8
Principles of Friction

• The coefficient of friction ? is related to the
  normal Force Fn and the force of Friction Ff.

Normal Force Fn Fw
Applied Force Fa
Friction Ff
Weight Fw mg
9
Problem involving Friction.
Normal Force Fn Fw
Friction Ff ?Fn
Tension
Tension
Weight Fwmg
Recall Newtons Second Law F ma.
Weight Fwmg
10
Problem Involving Friction

• The first mass (moving along the table)
• using F ma
• ? T - Ff m1a.
• The second mass (falling)
• using F ma
• Fw -T m2a.
• To find the tension or the acceleration, you need
  to solve these two equations simultaneously.

11
Work

• Work is the product of the Force exerted on an
  object (in the direction of motions) multiplied
  by the distance over which the force was exerted.
• W F ? dcos?

Force F
FN
?
Ff ?FN
F cos ?
Fw mg
Direction of Motion
12
Energy in Motion

• Gravitational Potential Energy
• The Energy of an object due to
• its position.
• GPE mgh
• where
• m mass of the body
• g acceleration due to gravity
• h height of the object above some reference
  level

• Kinetic Energy
• The energy of Motion
• KE ½ mv2
• where
• m mass of the body
• v velocity of the object.

13
Work-Energy Theorem

• The net work done on an object is equal to its
  change in kinetic energy. In other words, if the
  motion of an object changes, hence its kinetic
  energy changes, a force must have been applied to
  that object.

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Work-Energy Theorem

• But this can be extended to include the total
  energy of an object
• The work, W, done by all the other forces acting
  on a particle is equal to the total change in
  kinetic and potential energy of the particle.
• W ? Potential Energy ? Kinetic Energy.

15
Law of Conservation of Energy

• In an isolated system, the total energy of the
  system remains constant. This means that Energy
  may not be created or destroyed, but may be
  transferred from one form into another.
• G.P.E K.E. Constant.

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At the top of the slide, ET GPE KE GPE mgh
max KE ½ mv2 0 J
Children are doing work against gravity by
walking up the stairs. WFd Wmgh
As the children slide down GPE KE
At the bottom GPE 0 J KE max.
Work Done Change in Total Energy of the system
17
Conservation of Energy

• If the mass of an average child is 45kg, and the
  vertical height of the slide is 15m
• How much work was done by the children when
  walking up the stairs?
• What was the total energy of the child at the top
  of the slide?
• What was the speed of the child as she reached
  the bottom of the slide?

18
Conservation of Energy

• Solutions
• Data m 45kg h 15 m g 9.8 m/s2
• Find W using W Fd
• but F is the weight of the children and d is the
  vertical height
• ?W 45 x 9.8 x 15
• ?W 6615 J of work

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Conservation of Energy

• Work Done Change in the Energy.
• ET 6615 J
• The total energy of the children at the top is
  6615 J, which equates to the G.P.E of the
  children as they sit ready to go down the slide
• GPE 6615 J and KE 0 J since ET GPE KE
• ET GPE KE
• ? ET mgh ½ mv2 but at the bottom, GPE 0J
• ? 6615 0 ½ x 45 x v2
• ? v 17.1 m/s

20
Work and Power

• Power is often referred to as the rate of doing
  work.
• Power has the units of Watts
• 1 W 1 J/s
• Power is a scalar quantity.

21
Circular Motion.
Velocity - v

• Uniform circular motion is the motion of an
  object traveling at a constant (uniform) speed on
  a circular path.
• Whereas the magnitude of the velocity is
  constant, its direction is constantly changing,
  hence the object is accelerating.

Radius
22
Centripetal Acceleration.

• The centripetal acceleration of an object moving
  with a speed v on a circular path of radius r has
  a magnitude ac given by

v2
v1
Radius -r
v2
-v1
The centripetal acceleration vector is always
points towards the centre of the circle and
continually changes direction as the object moves.
Change in velocity ?vv2-v1
23
Centripetal Force.

• The centripetal force, Fc, is the net force
  required to keep an object of mass m, moving at a
  speed of v, on a circular path of radius r and
  has a magnitude given by

24
Tower of Terror

• The ride reaches speeds up 160 kph in seven
  seconds propelled by electro-magnetic forces
• The 'L'-shaped track stretches 330 metres
  horizontally - or the equivalent of three
  football fields.
• 100 metre vertical free-fall backward. You
  experience 6.5 seconds of weightlessness.

25
The Giant Drop

• The tallest free-falling ride in the world at
  120metres (39 storeys) high.
• Free fall time is 5 seconds. The cruise to the
  top takes approximately 90 seconds.Falling 120
  metres is the equivalent of falling from a
  39-storey building.
• What's stopping you? A sophisticated magnetic
  braking system stops the gondolas metres from the
  ground.

26
The Reef Diver

• The Reef Diver spins you vertically after picking
  up enough speed to keep you pinned to your seat.
  The measurements you make on this ride will
  reveal that the force you experience on the Reef
  Diver is continually changing while you are
  riding, which is what makes this ride so
  exhilarating.

27
The Vortex

• The Vortex pins you to the wall by spinning you
  around like a washing machine
• You are in an artificial gravitational field
  which
• You investigate this ride using measurements from
  the frame of reference of an observer, and that
  of a rider.