2. Warm Up
Explain what will happen if I release a bowling ball from my nose and let it swing back towards my face.

3. Energy Analysis Guiding Questions:
1. What is the system? 2. Where is the energy coming from? (Where is it stored?) 3. Where does the energy go, and/or what does it do? (How does it transfer?)

4. ESSENTIAL CONCEPTS A system is an object or a collection of objects.
For an isolated or closed system, conserved quantities are constant.

5. Work Energy transfer caused by a force exerted through a distance.
W = FΔxcosθ
Units
Work: Joule (J)
Force: Newton (N)
Displacement: meters (m)

6. Example
A student holds a psychology textbook , which has a mass if 1.5 kg, out of a second-story dormitory window and releases the book. How much work is done on the book by the student in holding it out the window?
How much work will have been done by the force of gravity during the time in which the book falls 3 m?

7. Work Done by a Variable Force
An example of a variable force doing work is stretching a spring.
As a spring is stretched (or compressed) the restoring force of the spring gets greater and an increasing applied force is required.
The applied F is directly proportional to the change in length of the spring.
Fs= -kΔx = -k(x-xo)
k is a spring constant of proportionality.
The greater the value of k, the stiffer or sronger the spring.
Units for k are newtons per meter (N/m)

10. Energy
Energy is a measure of the capability to produce change. By identifying the source of the change (ie, change in motion, position, shape, temperature, etc.) one can identify the means of energy transfer or storage.

11. Kinetic Energy
Kinetic Energy: energy stored due to the motion of an object.
K= 1/2mv2
Units
Energy: Joule (J)
Mass: kilogram (kg)
Velocity: meters per second (m/s)

12. Work-Energy Theorem: Kinetic Energy

13. Potential Energy Potential energy is energy of position.
As the name implies, an object having potential energy has the potential to do work.
Potential energy symbol is U.

14. Elastic Potential Energy
Energy storage due to a spring or elastic material.
Us=1/2kx2
Units
Energy: Joule (J)
Spring or force constant: Newton per meter (N/m)
Displacement: meters (m)

15. Gravitational Potential Energy
Gravitational Potential Energy: energy stored due to the object's position with respect to a reference level.
ΔUG = mgh
Units
Energy: Joules (J)
Mass: kilogram (kg)
Acceleration due to Gravity: meters/second squared (m/s2)
Displacement: meters (m)

16. Energy in Gravitational Systems
Potential energy is due to the relative positions of two objects.
How is frame of reference defined for “zero gravitational potential energy?”
For example, a ball lifted above the floor has gravitational potential energy only due to its position relative to the Earth; as the ball’s position relative to Earth changes, its gravitational energy changes.
The change in gravitational potential energy is independent of the path.
In most cases, the solution is based upon differences in potential energy and not an absolute value (i.e., gravitational potential energy calculated from center-to-center distance between Earth and an object).

19. Gravitational Potential Energy
Units
Energy: Joule (J)
Mass: kilogram (kg)
Distance: meters (m)
Universal Gravitational constant
G: 6.67x10-11 Nm2/kg2