1. Single particle system
Surroundings

2. Change in energy
System
The rest energy doesn’t change, unless the particle changes into another particle.
Surroundings

3. Example of a particle changing identity: beta decay of a neutron
Electron N P
Neutron
Proton
Antineutrino
We will only do problems in which particles do not change.

4. Change in energy
System
The rest energy doesn’t change, unless the particle changes into another particle.
Surroundings

5. Change in energy
A single particle, that doesn’t change into another particle, can only change its kinetic energy.
System
Surroundings

6. The energy principle for a single particle
Ignore these for now!
(friction, air drag, fluid drag…)
System
Surroundings

7. The energy principle for a single particle
System
Surroundings

8. Example:
What is the speed of the block after being pulled for 1.0 m? Assume it starts from rest. y x θ m
1.0 m

9. θ Example: System: block Surroundings: me (pulling on the block)
Assume there is no friction, so the table doesn’t do any work on the block. y x
System θ m
1.0 m

10. Example:
Find the speed of the ball after it falls through a given angle. m θ L
In this case, the component of the force along the direction of motion is changing, so we use calculus.

11. Example:
Break the path up into small parts. The ball moves a small angle Δθ for each part. m θ L
The work done for one small part is:

12. Example:
Break the path up into small parts. The ball moves a small angle Δθ for each part. m θ L
The work done for one small part is:

13. Example:
Break the path up into small parts. The ball moves a small angle Δθ for each part. m θ L
The total work is given by adding up the work for each small part:

14. Example:
Break the path up into small parts. The ball moves a small angle Δθ for each part. m θ L
The total work is given by adding up the work for each small part:

15. Example:
Break the path up into small parts. The ball moves a small angle Δθ for each part. m θ L
If we make , then the sum becomes an integral:

16. Example:
Break the path up into small parts. The ball moves a small angle Δθ for each part. m θ L
If we make , then the sum becomes an integral:

17. θ Example: ΔK = Wsurr m Kf – Ki = Wsurr L (1/2)mv2 = mgLsin
Energy principle:
ΔK = Wsurr m θ
Kf – Ki = Wsurr L
(1/2)mv2 = mgLsin
If we make , then the sum becomes an integral:
Solving the problem this way is much easier than using Newton’s 2nd Law!

18. Systems with more than one particle

19. Example:
A ball falling due to the Earth’s gravity.

20. System: ball
Surroundings: Earth
Let distance fallen = h.
Then Wsurr = Fg x h
= mgh
Energy principle:
ΔK = Wsurr
Kf – Ki = Wsurr
(1/2)mv2 = mgh

21. Same problem, different approach:

22. System: ball + Earth
Surroundings: none
This time, there is no external force acting on the system, so Wsurr = 0.
Energy principle:
ΔK = Wsurr = 0
This can’t be right!
What did we leave out?

23. Systems with more than one particle have another type of energy, that comes from internal interactions:
Potential energy 势能