ECP Chapter 5 PowerPoint

1. Chapter 5
Work and Energy

2. Chapter 5 Objectives
• Understand work and how it is computed
• Relate work and kinetic energy
• Explain potential and kinetic energy
• Apply the principle of conservation of
mechanical energy
• Explain power and distinguish it from energy.

3. Work Demonstrations
• Lifting the block
• Dropping the block
• Pushing the block along the counter
• Letting the block slide to a stop
• Pushing the block into the counter
• Carrying the block across the room

4. Definition of Work (95)
xW F x  
Work, J (Joules)
Component of the force parallel
to the displacement, N
Displacement, m

5. Net Work (95)
• Each force does its own work
• Figure 5.1 (95)
• Figure 5.2 (95)

6. Work Problems (95)
• Example 5.1 (95)
• Example 5.2 (96)
• Conceptual Example 5.3 (98)

7. Work Done by Gravity (98)
• Substitute into W=Fx
• Both weight and are negative, so work is
positive as the object drops
y
gW m g y    
Work done by gravity, J
Acceleration due to
gravity, 9.8 m/s2
Mass, kg
Vertical displacement, m

8. Work Done by Gravity Example (99)
• Example 5.4 (99)

9. Work Done by a Variable Force (100)
• Work done by a constant force
• Work done by a variable force
• A calculus problem

10. Hooke’s Law (100)
• Hooke’s Law demonstration

11. Hooke’s Law (100)
xF k x 
Force required to stretch
the spring by length x, N
Force constant of the
spring, N/m
Displacement of the spring
from equilibrium, m

12. Work Done on a Spring (101)
21
2W k x  
Work done in stretching
the spring through a
displacement x, J
Force constant of the spring, N/m
Displacement from
equilibrium, m

13. Springs and Newton’s Third Law (101)
• The stretching force and the restoring force
are a Newton’s Third Law pair
• The stretching or applied force does positive
work
• The restoring force does negative work

14. Deriving the Work-Energy Theorem
(102)
• Start with the definition of work
• Substitute from Newton’s Second Law
net netxW F x  
net xW m a x   

15. Deriving the Work-Energy Theorem
(102)
• Recall the kinematics formula
• Solve for and substitute into the
previous equation
2 2
x 0x xv v 2 a x    
xa x 
 2 21
x x 0x2a x v v   
 2 21
net x 0x2W m v v   

16. Deriving the Work-Energy Theorem
(102)
• Distribute to obtain:
• We define kinetic energy:
2 21 1
net x 0x2 2W m v m v     
21
2KE m v  
Kinetic Energy, J
Mass, kg
Velocity, m/s

17. The Work-Energy Theorem (103)
• Therefore, the Work-Energy Theorem states
that the net work done on an object is
equally to the change in kinetic energy of the
object.
• Kinetic energy is the energy of motion.
• Every moving object has kinetic energy

18. Gravitational Potential Energy (105)
• The opposite of work done by gravity
• Choose an arbitrary point to measure Δy
from
• It should be the lowest point in the problem
GPE m g y   
Gravitational Potential
Energy, J
Mass, kg
Acceleration due to
gravity, 9.8 m/s2
Change in
vertical
position, m

19. Elastic Potential Energy (107)
• The energy stored in a spring
• The spring may be either compressed or
stretched
21
2EPE k x  
Elastic potential energy, J
Force constant of the spring, N/m
Displacement from
equilibrium, m

20. Conservative Forces (105)
• If the work done by a force on an object
moving between two points does not depend
on the path taken, the force is conservative
• Examples: contact forces, tensions, gravity,
magnetism

21. Nonconservative Forces (105)
• If the work done by a force on an object
moving between two points depends on the
path taken, the force is nonconservative.
• Examples: friction, drag, thrust

22. Law of Conservation of Mechanical
Energy (108)
• The total original mechanical energy of a
system plus any work done by nonconserva-
tive forces is equal to the total final
mechanical energy of the system.
1 1 1 2 2 2KE GPE EPE W KE GPE EPE     

23. Solving Energy Problems (109)
• Draw a picture of the problem
• Label the energies at position one
• Label the energies at position two
• Label any work done by nonconservative
forces in between positiosn one and two
• Substitute into the conservation law and
solve

24. Energy Problems (109)
• Example 5.9 (109)
• Example 5.10 (110)
• Example 5.11 (111)
• Example 5.12 (112)

25. Energy-Projectile Motion Lab
• Purpose: Use energy to predict the range of a
projectile
• The set up:

26. Power (112)
• Power is the rate of doing work
• A Watt is a joule/s
W
P
t

Power, W Work, J
Time, s

27. Average Power (113)
• An alternate formula
x xP F v 
Average power, W
Force parallel to the velocity, N
Average velocity, m/s

28. Power Problems (114)
• Example 5.13 (114)
• Example 5.14 (114)

29. Chapter 5 Problem Sets
• Honors: P. 117, Ex. 28, 30, 34, 40, 46, 58, 66,
68, 72, 74, 84, 88, 98, 102, 118
• UConn: P. 117, Ex. 28, 30, 34, 40, 46, 58, 64,
66, 68, 72, 74, 84, 88, 94, 98, 102, 118, 124