1. Chapter 7 Conservation of Energy

2. Recap – Work & Energy The total work done on a particle
is equal to the change in its
kinetic energy

3. Potential Energy
The total work done on an object equals the change in its kinetic energy
But the total work done on a system of objects may or may not change its total kinetic energy. The energy may be stored as potential energy.

4. Potential Energy – A Spring
Both forces do work on the spring. But
the kinetic energy of the spring is
unchanged. The energy is stored as
potential energy

5. Conservative Forces If the ski lift takes you up a displacement h, the
work done on you, by
gravity, is –mgh. But when you ski downhill
the work done by gravity
is +mgh, independent of the
path you take

6. Conservative Forces The work done on a particle by
a conservative force is independent of the path taken
between any two
points

7. Potential-Energy Function
If a force is conservative, then we can
define a potential-energy function as the
negative of the work done on the particle

8. Potential-Energy Function
potential-energy function associated
with gravity (taking +y to be up)
The value of
U0 = U(y0)
can be set
to any
convenient
value

9. Potential-Energy Function of a Spring
By convention,
one chooses
U0 =U(0) = 0

10. Force & Potential-Energy Function
In 1-D, given the potential energy function
associated with a force one can compute
the latter using:
Example:

11. 7-1 Conservation of Energy

12. Conservation of Energy
Energy can be neither
created nor destroyed
Closed System
Open System

13. Conservation of Mechanical Energy
If the forces acting are conservative
then the mechanical energy is
conserved

14. Example 7-3 (1) How high does the block go? Initial mechanical energy
of system
Final mechanical energy
of system

15. Example 7-3 (2) Forces are conservative, therefore,
mechanical energy is conserved
Height reached

16. Example 7-4 (1) How far does the mass drop? Initial mech. energy
Final mech. energy

17. Example 7-4 (2)
Final mech. energy = Initial mech. energy

18. Example 7-4 (3)
Solve for d
Since d ≠ 0

19. Example 7-4 (4) Note is equal to loss in gravitational potential
energy

20. Conservation of Energy & Kinetic Friction
Non-conservative forces, such as kinetic friction, cause mechanical energy to be transformed into other forms of energy, such as thermal energy.

21. Work-Energy Theorem Work done, on a system, by external
forces is equal to the change in energy
of the system
The energy in a system can be
distributed in many different ways

22. Example 7-11 (1) Find speed of blocks after spring is
released. Consider spring & blocks
as system. Write down initial energy.
Write down final energy.
Subtract initial
from final

23. Example 7-11 (2) Initial Energy Take potential energy of system
to be zero initially
Kinetic energy of
system is zero
initially

24. Example 7-11 (3) Final Energy Kinetic and potential energies of
system have changed

25. Example 7-11 (4) Subtract initial energy from final energy
But since no
external forces
act, Wext = 0, so
Ef = Ei

26. Example (5)
And the answer is…
Try to derive
this.

27. E = mc2 E = mc2 In a brief paper in 1905 Albert Einstein wrote
down the most famous
equation in science
E = mc2

28. Sun’s Power Output Power 1 Watt = 1 Joule/second
100 Watt light bulb = 100 Joules/second
Sun’s power output
3.826 x 1026 Watts

29. Sun’s Power Output Mass to Energy
Kg/s = x 1026 Watts / (3 x 108 m/s)2
The Sun destroys mass at
~ 4 billion kg / s

30. Problems
To go…

31. Ch. 7, Problem 19

32. Ch. 7, Problem 29

33. Ch. 7, Problem 74