Work

1
Work Energy

• Chapter 7

2
Work Energy

• Energy the ability to do work
• Forms chemical, mechanical, electromagnetic,
  nuclear, thermal
• Examples kinetic energy, elastic potential
  energy, gravitational potential energy
• Units Joules (J) (equivalent to Nm)

3
Work Energy

• Work is the link between energy and force
• Work definition 2 the transfer of energy from
  one form to another or from one object to another
• Work definition 3 the bridge between energy
  forms

4
Work Energy

• Work Definition 1 The product of the force
  acting upon an object and the distance that the
  object moves as a result
• W (FcosT) d ? Textbook
• F applied force
• s, d displacement of object
• T angle between applied force and displacement
• Units Newton-meter

5
Work Energy

• What is the work done on this box to have it
  raised 10 m?

W FcosT s W (20 N cos 0º) (10 m) W 200 Nm
2 kg
6
Work Energy

• What is the work done on this box to have it
  moved 10 m horizontally?

40 N
W FcosT s W (40 N cos 25) 10m W (36.3 N)
(10 m) W 363 Nm
25º
20 kg
7
Energy and Force

• Hookes Law The force applied by a spring is
  directly related to its displacement from its
  equilibrium length.
• F -kx
• F force applied by spring
• k spring constant
• X displacement (with direction) from
  equilibrium position

8
Finding Energy

• Link to work ? Energy Work (when no energy
  lost as heat)
• Kinetic Energy energy of motion
• KE ½ mv2
• Gravitational Potential Energy energy due to
  position vertically
• GPE mgh

9
Finding Energy

• Elastic Potential Energy energy due to
  elongation or compression of a spring
• EPE ½ kx2
• k spring constant
• units N/m
• x displacement of spring (m)
• (compression or elongation)

10
Objects Moved by Springs

• Objects moved continually by springs are subject
  to the Law of Conservation of Energy
• Over any time interval, total mechanical energy
  stays constant

11
Work Energy

• To find work upon a system, find change in
  kinetic energy
• W ?KE KEf KEi
• Example if objects KE has increased from 300 J
  to 500 J, then 200 Nm of work has been performed
  upon it

12
Work, Energy, Power

• Power The rate at which work is being done
• P W / t
• Units Watts (W) 1 W 1 J/s
• Energy P x t
• J/s x s

13
Work, Energy, Power

• Horsepower is English version of power
• Developed by James Watt to help gauge success of
  his new invention, the steam engine
• Created by analyzing horse performance in
  operating coal mine water pumps
• Horses 360 ft lbs / s
• 1 Horsepower (HP) 550 ft lbs / s

14
Finding Power in Watts

• Find the power necessary to raise the block
  vertically 10 m in 5.0 s.

W FcosT s W (20 N cos 0º) (10 m) W 200 Nm
P W / t 200 Nm / 5.0 s 200 J /
5.0 s 40 Watts
2 kg
15
Motion and Power Example

• What is the power applied by a car engine if a
  car proceeds against a frictional force of 200 N
  but still sustains a 30 m/s (67 mph) speed on the
  tollway? What work is done by this engine in a
  20 min span?

16
Work-Energy Theorem

• The work performed on an object is equal to the
  change in kinetic energy experienced by a system
  over time
• W ?KE KEf KEi

17
Example Use Forces or Energy

• What frictional force is applied upon an object
  of mass 10 kg that slows from a speed of 2.0 m/s
  to a stop on a horizontal surface in a 20 m
  distance? (No other x forces exist)

18
What frictional force is applied upon an object
of mass 10 kg that slows from a speed of 2.0 m/s
to a stop on a horizontal surface in a 20 m
distance? (No other x forces exist)

• Vf2 Vi2 2ax
• a - 0.100 m/s2
• Fnetx Ff m ax
• Ff -1.0 N

19
What frictional force is applied upon an object
of mass 10 kg that slows from a speed of 2.0 m/s
to a stop on a horizontal surface in a 20 m
distance? (No other x forces exist)

• W ? KE
• FAcosT s KEf - KEi
• FA cos 180(20 m) ½ mvf2 1/2mvi2
• F (-1) (20 m) 0 ½ (10 kg)(2 m/s)2
• F (-20 m) 20 kgm/s2 x m
• F -1 N

20
Example of Work-Energy Theorem

• 20 J of work is done on an object that weighs 40
  N and is moving 10 m/s to start with. What is
  the objects final velocity?