1. Potential Energy and Conservation of Energy
Chapter 8
Potential Energy and Conservation of Energy
8-6 Conservation of Energy
8-1 Work and Potential Energy
8-2 Path Independence of Conservative Forces
8-3 Determining Potential Energy Values
8-4 Conservation of Mechanical Energy
8-5 Work Done on a System by an External Force and
Thermal Energy due to Friction

2. 8-6 Conservation of Energy Energy of a System
Work Kinetic Energy Theorem
For a Single Object:
Conservation of Energy Principle
For a system of objects
Change in Kinetic energy
Change in Energy
Work done by an (external) force on the object/system
Change in Kinetic energy
Change in Potential energy
Change in thermal energy
Change in internal energy
However we will not worry about DEint
in phys101, and we’ll deal only with situation where DEint =0

3. 8-6 Conservation of Energy
Energy of a System
A particle-earth system
A spring-block system
Fext Fg
Fext Fs
Fg is not an external force
Fs is not an external force
If we choose our system to be a particle or a block only, then Fg and Fs will be an external force to our system (which is a single body now)

4. A particle-earth system
8-2 Work and Potential Energy
Gravitational Potential Energy
A particle-earth system Fg Fg
initial
final
If Fext = 0 for this system then W = 0, but we know that DK is not zero as the ball falls.. So where is the energy coming from to increase its kinetic energy?
We associate what is called a Potential Energy Ug with the configuration of the earth particle system, the change of which is the negative of the work done by gravitational force: DUg = -Wg

5. 8-3 Path Independence of Conservative Forces Conservative Forces
Work done by a conservative force does not depend on the path between the initial and final point. W1
W1=W2 W2
In another words:
The net work done by a conservative force on a particle moving around any closed path is zero.
Conservative Force
Non-Conservative Force
Gravitational Force
Frictional Force
Spring Force
Drag force
W=0

6. 8-3 Path Independence of Conservative Forces Non-Conservative Forces
Work depends on the path
Example:

7. 8-3 Determining Potential Energy Values Definition of Potential Energy
It is defined for a system of two or more objects
It is defined only for conservative forces
Gravitational Potential Energy, Ug
Elastic Potential Energy, Us

8. 8-3 Determining Potential Energy Values Checkpoint
A particle moves from x =0 to x=1, under the influence of a conservative force as shown. Rank according to DU, most positive first (descending order).

9. 8-3 Determining Potential Energy Values Example
What is the U of the sloth-earth system if our reference point is
at the ground
at a balcony floor that is 3.0 m above the ground
at the limb
1 meter above the limb?

10. 8-4 Conservation of Mechanical Energy Mechanical Energy
Emech = K+U
Mechanical energy
Potential energy
Kinetic energy
If there is no external acting on a system (W = 0) and its thermal energy is constant (no non-conservative forces such as friction, DEth = 0), then its mechanical energy is conserved.
Mechanical Energy is conserved
0 = DK+DU OR
Kf+Uf= Ki+Ui=constant

11. 8-4 Conservation of Mechanical Energy Checkpoint
Rank according to speed at point B. Ball sliding on a Frictionless Ramp

12. 8-4 Work Done on a System No friction involved
We have a block-floor-earth system. The applied force F is external to the our system. The law of conservation of energy states that the work done by external force on a system is equal to the change of energy
W = DE
same height
Fd= DK+DU

13. 8-4 Work Done on a System friction involved
We have a block-floor-earth system, this time there is friction. The friction force is now an internal force. However as a result of the friction force, there will be a loss in the kinetic energy which appear as an increase in the thermal energy (converted to heat) of the system.
W = DE
It can be shown that the change in thermal energy is equal to the negative of the work done by the friction force: DEth= fk d = - Wf
W = DEmech+DEth
Therefore the conservation of energy principle can also be stated in the form: W + Wf = DEmech
F d= DK+DU+DEth
fk d

14. 8-4 Work Done on a System Example
By what distance d is the spring compressed when the block stops?
W = DEmech+DEth OR
W + Wf = DEmech
DEth = - Wf = fk d