1. Kinetic Energy and Gravitational Potential Energy We can rewrite
Chapter 10 Energy
Kinetic Energy and Gravitational Potential Energy
We can rewrite

2. Kinetic Energy:
We define K = ½ mV2
Unit of kinetic energy (Kg m2/s2) Joule
Ex. For a mass 0.5 Kg, V = 4m/s, K = 4J
Gravitational potential energy:
• We define Ug=mgy
• Unit of potential energy: Joule
• Kinetic energy never be negative.
• gravitational potential energy depends on the position.

3. Example 10.3 P275 Example 10.4 P276 Example 10.8 P283
Stop to think P273 Stop to think P275 Stop to think P278 Stop to think P280 Stop to think P284 Stop to think P292
Example P275
Example P276
Example P283
Example P286
Example P291

4. Perfectly Inelastic collision

5. Elastic Collisions
Perfectly elastic collision conserves both momentum and kinetic energy
Momentum conservation
Kinetic energy conservation

6. Perfectly elastic collision with ball 2 initially at rest
Solve above equations, the solution is
Question: If m1=m2, Vi1=V, m2 initially at rest, after collision what is
Vf2, Vf1

7. Gravitational potential energy
mgh
Y or (h) depends on where you choose to put the origin of your coordinate system.
But potential energy change ΔU is independent of the coordinate system

8. Energy Bar Chart

9. If we neglect air resistant or friction:

10. Quick think
A small child slides down the four frictionless slides A-D. Each has the same height.
Rank in order. From largest to smallest her speeds VA to VD at the bottom.
VA = VB =VC =VD

11. Ex A ballistic pendulum A 10 g bullet is fired into a 1200g wood block hanging from a 150-cm-long string. The bullet embeds itself into the block, and block then swings out to an angle of 40o. What was the speed of the bullet?
The momentum conservation equation
Pi = Pf applied to the inelastic collision
Then turning our attention to the swing
The energy equation
Kf + Ugf = Ki + Ugi
We define y1 = 0
Get:

12. Three identical balls are thrown from the top of a building, all with the same initial speed the first is thrown horizontally, the second at some angle above the horizontal and third at some angle below the horizontal. Neglecting the air resistance, rank the speeds of the balls at the instant each hits the ground .
Answer: All the three balls have the same speed at the moment they hit the ground.
Since neglect the air resistance, total mechanical energies for each ball should be conserved.
Ki+Ui= 1/2mvi2 +mgh
Kf + Uf = 1/2mvf2
Ki+Ui = Kf +Uf
Vf2= 2gh + vi2 does not matter the angle.
Three balls take different times to reach the ground

13. Ex The speed of sled

14. A rebounding pendulum

15. Restoring forces and Hooke’s Law
Displacement from equilibrium ∆s
Hooke’s Law
K is called the spring constant. It is spring character, unit:N/m

16. Measure spring constant k

17. Spring potential energy

18. Conservation of mechanical energy
Mechanical energy E (mech) = K + U
If there is no friction or other losses of mechanical energy then ΔE(mech)=0
This is the law of conservation of mechanical energy

19. Energy Diagrams Particle in free fall
Energy Diagram is used to visualize motion.

20. A mass oscillating on a spring

21. More general energy diagram
How to get kinetic energy from this diagram?