Machines

1
Machines

• Simple Machines (End of Mechanics for this year
  in Physics 1)
• Simple machines are good examples of the
  interrelationship between force, energy, and work
• A lever or pulley is a simple machine to multiply
  or change the direction of a force BUT
• work inputwork output
• (force X distance)input (force X
  distance)output
• A lever or a pulley can multiply
  force..how?...remember work input work output

80N
1 m
1/8 m
10N
2
Machines

• Simple Machines
• Pulleys
• A kind of lever that can
• Can change the direction of a force
• Multiply force
• When combined with another pulley
• Change direction and multiply the force
• Other examples of Simple Machines???

3
Machines

• Simple Machines
• Harry the painter swings year after year from his
  bosun's chair. His weight is 500N and the rope,
  unknown to him, has a breaking point of 400N.
• Why doesn't the rope break when he is supported
  as shown to the left on the above picture?
• One day Harry is painting near a flagpole, and,
  for a change he ties the free end of the rope to
  the flagpole instead of to his chair as shown to
  the right.
• Why did Harry end up taking his vacation early?
  (Not really funny! Too bad!)

4
Machines

• Simple Machines
• Actual Mechanical Advantage (AMA)
• Ratio of output force to input force
• AMA for a pulley number of strands of
  cable/rope that actually support the load
• Pulley examples on board

5
Machines

• Simple Machines
• Efficiency
• Any real machine is not 100 efficient
• There are always losses of energy
• Therefore efficiency is always less than 1
• Automotive example
• Fuel energy in (100) cooling water losses
  (35)-Engine output (30)-exhaust heat (35)
• Other examples?

6
Torque

• Torque
• A torque is a force exerted at a distance from an
  axis of rotation the easiest way to think of
  torque is to consider a door. When you open a
  door, where do you push? If you exert a force at
  the hinge, the door will not move the easiest
  way to open a door is to exert a force on the
  side of the door opposite the hinge, and to push
  or pull with a force perpendicular to the door.
  This maximizes the torque you exert.
• We can state the equation for torque as

7
Torque

• Torque
• In a given situation, there are usually three
  ways to determine the torque arising from a
  particular force. Consider the example of the
  torque exerted by a rope tied to the end of a
  hinged rod, as shown in the diagram.
• The first thing to notice is that the torque is a
  counter-clockwise torque, as it tends to make the
  rod spin in a counter-clockwise direction. The
  rod does not spin because the rope's torque is
  balanced by a clockwise torque coming from the
  weight of the rod itself.
• There are three equivalent ways to determine this
  torque, as shown in the diagram below.
• Method 1 - In method one, simply measure r from
  the hinge along the rod to where the force is
  applied, multiply by the force, and then multiply
  by the sine of the angle between the rod (the
  line you measure r along) and the force.
• Method 2 - For method two, set up a right-angled
  triangle, so that there is a 90 angle between
  the line you measure the distance along and the
  line of the force. This is the way the textbook
  does it done in this way, the line you measure
  distance along is called the lever arm. If we
  give the lever arm the symbol l, from the
  right-angled triangle it is clear that

8
Torque

• Center of Gravity
• Center of gravity
• The center of gravity of an object is the point
  you can suspend the object from without there
  being any rotation because of the force of
  gravity, no matter how the object is oriented. If
  you suspend an object from any point, let it go
  and allow it to come to rest, the center of
  gravity will lie along a vertical line that
  passes through the point of suspension. Unless
  you've been exceedingly careful in balancing the
  object, the center of gravity will generally lie
  below the suspension point.
• The center of gravity is an important point to
  know, because when you're solving problems
  involving large objects, or unusually-shaped
  objects, the weight can be considered to act at
  the center of gravity. In other words, for many
  purposes you can assume that object is a point
  with all its weight concentrated at one point,
  the center of gravity.
• For any object, the x-position of the center of
  gravity can be found by considering the weights
  and x-positions of all the pieces making up the
  object
• COG
• A similar equation would allow you to find the y
  position of the center of gravity.
• The center of mass of an object is generally the
  same as its center of gravity. Very large
  objects, large enough that the acceleration due
  to gravity varies in different parts of the
  object, are the only ones where the center of
  mass and center of gravity are in different
  places.
• Neat facts about the center of gravity
• Fact 1 - An object thrown through the air may
  spin and rotate, but its center of gravity will
  follow a smooth parabolic path, just like a ball.
  
• Fact 2 - If you tilt an object, it will fall over
  only when the center of gravity lies outside the
  supporting base of the object.
• Fact 3 - If you suspend an object so that its
  center of gravity lies below the point of
  suspension, it will be stable. It may oscillate,
  but it won't fall over.