1. 7 Conservation of Energy
Potential Energy
The Conservation of Mechanical Energy
The Conservation of Energy
Mass and Energy
Hk: 23, 27, 39, 47, 55, 65, 69, 71

2. Potential Energy Potential Energy is stored energy
Potential Energy is position dependent (KE is speed dependent)
Ex. object at higher height has more PE
Types of PE: gravitational, elastic, electric, magnetic, chemical, nuclear. /

3. Conservative Forces
When the work done by a force moving from position 1 to 2 is independent of the path, the force is Conservative.
The work done by a Conservative Force is zero for any closed path.
Conservative Forces have associated Potential Energies /

4. Non Conservative Forces
Produce thermal energy, e.g. friction
Work done by Non Conservative Forces is path dependent, e.g. longer path, more work required /

5. Potential Energy Functions

6. Elastic Potential Energy

7. Ex. Elastic Potential Energy
100N/m spring is compressed 0.2m.
F = -kx = -(100N/m)(0.2m) = -20N
U = ½kx2 = ½(100N/m)(0.2m)2 = 2J /

8. Gravitational Potential Energy

9. Ex. Gravitational Potential Energy
Ex: A 2kg object experiences weight (2kg)(9.8N/kg) = 19.6N.
At 3m above the floor it has a stored energy of mgy:
(2kg)(9.8N/kg)(3m) = 48.8Nm = 48.8J. /

10. Conservation of Energy
Individual energy levels change.
Sum of all individual energies is constant. /

11. Conservation of Mechanical Energy

12. KE E Ug

13. Ex. Conservation of Mechanical Energy: Object dropped from height h above floor.

14. Energy E1 E2 E3
Kinetic
½mv22
PE-g
mgh
PE-spring
½kx2
Totals 1 2 3

15. y y Energies and speeds are same at height y
Energy
E(h)
E(y)
Kinetic
½mv2
PE-g
mgh
mgy
Totals
½mv2 + mgy
Energies and speeds are same at height y
Accelerations at y are not same y y

16. Work Energy with Friction

17. Energy Ei Ef
Kinetic
½mvi2
PE-g
Thermal
fks
Totals
Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping. s

18. A 2. 00kg ball is dropped from rest from a height of 1
A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie-frame type diagram of the motion is shown below. 1 2 5 4 3
Type E1 E2 E3 E4 E5
gravita-tional
mg(1)
mg(1/2)
kinetic
½ m(v2)2
½ m(v4)2
elastic
PE-elastic
thermal
E-thermal

19. Calculate v2: (use 1st and 2nd columns) mg(1) = ½ m(v2)2. g = ½ (v2)2.
By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J
Calculate v2: (use 1st and 2nd columns)
mg(1) = ½ m(v2)2.
g = ½ (v2)2.
v2 = 4.43m/s
Calculate PE-thermal: (use 1st and 5th columns)
mg(1) = mg(1/2) + PE-thermal
mg(1/2) = PE-thermal
PE-thermal = 9.8J

20. Calculate PE-elastic: (use 1st and 3rd columns)
PE-elastic + PE-thermal = mg(1)
PE-elastic = 19.6
PE-elastic = 9.8J
Calculate v4: (use 1st and 4th columns)
½ m(v4)2 + PE-thermal = mg(1)
½ m(v4) = 19.6
½ m(v4)2 = 9.8
(v4)2 = 2(9.8)/2
v4 = 3.13m/s

21. Potential Energy & Force

22. Equilibrium
Stable: small displacement in any direction results in a restoring force toward Equilibrium Point
Unstable: small displacement in any direction results in a force away from Equilibrium Point
Neutral: small displacement in any direction results in zero force

23. Mass and Energy

24. Efficiency & Thermodynamics

25. Summary Potential Energy function & force
The Conservation of Mechanical Energy
The Conservation of Energy
Mass and Energy /