Work

1
Work and Energy

• Work
• and
• Energy
• Updated 10/27/06

2
Work

• Work product of the force along the line of the
  displacement, and the magnitude of the
  displacement.
• W Fs (cos ?)
• where ? is the angle between F and s

3
Work
work force x displacement W Fd Displacement
must be parallel to the force. No Force No
work No Displacement No work
4
Work

• Work is done Lifting against gravity
• Sliding against friction
• Compressing a spring
• Extending a spring

5
Work

• The area under a force-displacement graph is the
  work done.

6
Work and Energy

• units are Joules
• Joules Newtons x meters
• Newtons x meters kg m2/s2
• --------------------------------------------------
  -
• Alternate units
• c-g-s system dyne x centimeter or erg
• English foot x pound or foot-pound

7
Energy

• Energy appears in many forms. Initially we are
  dealing with mechanical (kinetic) and potential
  energy (gravitational and elastic).
• gravitational PE weight x height
• PEG mgh
• units are in Joules

8
Energy

• elastic PE
• ½ x (spring constant) x (displacement)2
• PESPRING ½ kx2
• units are also in Joules

9
Energy

• kinetic energy ½ x (mass) x (speed)2
• KE ½ mv2
• units are also in Joules

10
Energy

• Conservation of Mechanical Energy
• (KE PEG PES)initial (KE PEG PES)final
• KE kinetic energy
• PEG gravitational potential energy
• PES elastic potential energy

11
Work and Energy

• Work-Kinetic Energy Theorem
• The net work done on an object by a net force
  acting on it is equal to the increase in the
  kinetic energy of the object.
• Wnet KEf - Kei ?KE
• where KE ½ mv2

12
Work and Energy

• Work-Kinetic Energy Theorem
• Positive net work is work done on an object or
  system by a net force acting on it.
• Negative net work is work done by an object or
  system.

13
Work and Energy

• Gravitational Potential Energy
• The net work done by an object is equal to the
  reduction in the potential energy of the object.
• WG - (PEf - PEi) - ?PE
• where PE mgh

14
Work and Energy

• Therefore.
• Work (KEf - KEi) (PEf - PEi)
• where PE mgh
• and KE ½ mv2

15
Power

• Power The rate at which work is done. Work
  divided by the time interval during which the
  work is done.
• power work done
• time interval
• Units are Watts, which is one Joule of work in
  one second.

16
Machines

• Machine A device used to multiply forces or
  change the direction of the forces.
• Inclines Ramps, Screws
• Pulleys
• Levers Type 1, Type 2, Type 3

17
Machines
18
Machines
Class 1 Lever Class 2 Lever
19
Machines
Class 3 Lever
20
Machines
Basic Pulley (Changes Direction)
21
Machines
Basic Pulley x 2 Mechanical Advantage equals
of ropes holding load
22
Machines
Ramp Mechanical Advantage equals distance (d)
/ height (h)
23
Machines

• mechanical advantage force output
• force input
• The mechanical advantage gives the multiplier for
  the force you use to do work. It is the inverse
  of the distance traveled by the object.

24
Machines

• Ideal Machine A machine that is 100 efficient.
• efficiency useful work output or
• useful work input
• efficiency actual mechanical advantage
• theoretical mechanical advantage

25
Work and Energy

• End of
• Work
• and
• Energy