Work and Energy

1
Work and Energy

• Chapter 6

2
Energy

• The ability to do work, measured in Joules (J),
  scalar
• mechanical (potential and kinetic)
• heat
• electrical
• nuclear
• chemical

3
Work

• A force applied over a distance. The object must
  move in the same direction as a component of the
  applied force.
• Scalar can be added algebraically assuming that
  the force is constant.
• W F (cos ?) s s distance in m
• Be careful with the ?, this makes the magnitude
  of W either or -

4
Simple Machines

• Use mechanical advantage to perform the same
  amount of work but multiply the input force by
  changing direction, input distance, or radius.

Pulley Applet
5
Types of Energy

• Mechanical ME- sum of potential and kinetic
  energies (scalar)
• ME PE KE

6
Types of Energy

• Potential (PE)- several types
• Gravitational PE - due to distance above a zero
  level (scalar)
• PEg mgh m is mass in kg
• h is height in m
• Elastic PE restoring energy in a spring
  (scalar)
• PEE 1/2kx2

7
Types of Energy

• Kinetic KE - due to motion (translational and
  rotational) (scalar)
• KE 1/2mv2 (translational)

8
Conservation of Mass/Energy

• Mass/Energy cannot be created or destroyed only
  converted from one form to another.
• E mc2
• In most problems, the concern is whether or not
  mechanical energy is conserved. To decide this,
  determine what types of forces are present in the
  system.

9
Conservative or Non-conservative

• Conservative forces- the work done is independent
  of the path taken
• ex. gravity, normal, springs, etc.
• Non-conservative forces -the work done is
  dependent of the path taken
• ex. friction, tension
• Work done by Gravity (conservative) Wg
  mg(ho-hf)
• Mechanical energy is conserved if only
  conservative forces are doing work on a system!

10
Conservation of Mechanical Energy

• Conservation of Mechanical Energy
• KEf PEf KEo PEo
• 1/2mvf2 mghf 1/2mvo2 mgho

• If non-conservative forces are doing work on a
  system, the magnitude of the work is equal to the
  difference between the initial and final values
  of the mechanical energies.

11
Work Done by Non-conservative Force

• Wnc (KEf PEf) - (KEo PEo)
• Wnc (1/2mvf2 mghf) - (1/2mvo2 mgho)

12
Work Energy Theorem

• If potential energy isnt changing, the total
  work done is equal to the ?KE
• WT KEf - KEo

13
Work by a Variable Force

• Work by a variable force - springs, stretchable
  materials, etc.
• Two methods for solving graphing or integration
• Graphing

14
Power

• Rate at which work is done measured in Watts (W)
  or horsepower (hp)
• 1 hp 746 W (scalar)
• P W/t
• P
• P