1. Ch 6 Work and Energy

2. Work in 1 dimension
Work is when a force is applied and an object is displaced
If no displacement occurs or no force is applied then no work is done.
The definition of work when the force is parallel to the displacement

3. In the SI system, the units of work are joules:
As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion.

4. Work in 2 dimensions
If the force is at an angle to the displacement you must determine the component of the force that is directed parallel to the displacement.

5. Work done by forces that oppose the direction of motion, such as friction, will be negative.
Fpx
-Ffr

6. The work done may be positive, zero, or negative, depending on the angle between the force and the displacement

7. If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force
Wtotal=W1 + W2 + W3 … = Σ W

8. 6-3 & 6-4 KE, PE and Work Energy Principle
Kinetic energy (KE) is energy of motion
Gravitational potential energy (PE; often just called potential energy) is energy of position

9. ME= KE + PE Work and Energy
Mechanical Energy is the sum of the kinetic and potential energy of an object
Energy was traditionally defined as the ability to do work.
Not all forces can do work, but ME can
ME= KE + PE

10. KE=1/2mv2 Kinetic Energy KE
For objects moving at speeds much slower than the speed of light Kinetic energy is calculated by
KE=1/2mv2

11. PE=mgy Potential Energy PE
An object can have potential energy by virtue of its position or height
A wound-up spring
A stretched elastic band
An object at some height above the ground
PE=mgy

12. Work-Energy Principle or Theorem
The net force done on an object is equal to the change in the object’s kinetic energy
Work and kinetic energy can be equated and have the same units; joules.
Wnet=ΔKE

13. Potential energy can also be stored in certain materials when they are compressed; the figure below shows potential energy yielding kinetic energy.

14. Hooke’s Law The force required to compress or stretch a spring is:
where k is the spring constant, and needs to be measured for each spring.
Negative because it is a restoring force, acting in the opposite direction of displacement

15. Elastic potential energy
The force increases as the spring is stretched or compressed
Potential energy of the compressed or stretched spring measured from its equilibrium position

16. 6-5 Conservative and Nonconservative Forces
Conservative forces are ones that do not depend on, or are independent, of the path taken. An example is gravity
If the object were to return to the starting point no net work would be done

17. Nonconservative forces are ones that do depend on the path taken.
Also called dissipative forces because the energy is not stored as mechanical energy but changed into a different type such as heat energy
An example is friction

18. Potential energy can only be defined for conservative forces.

19. This is the principle of conservation of mechanical energy
6-6 Mechanical Energy and Its Conservation
If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero
If only conservative forces are acting the total ME of the system stays constant or is conserved
This is the principle of conservation of mechanical energy

20. Total mechanical energy ME= KE + PE therefore

21. This is the Law of Conservation of Energy
Energy conservation
The total energy is neither increased nor decreased, only transformed from one form to another and transferred from one object to another. The total amount remains the same.
This is the Law of Conservation of Energy

22. Power is the rate at which work is done
In the SI system, the units of power are watts:
The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.

23. Efficiency Efficiency=Poutput Pinput
The ratio of power output to input
Always less than 1 because engines always lose some input power to friction
Efficiency=Poutput
Pinput

24. References
Giancoli, Douglas. Physics: Principles with Applications 6th Edition
Walker, James. AP Physics: 4th Edition. 2010