1. Lecture 09: Work and Kinetic Energy
Energy Overview
Conservation of Energy
Forms of Energy
Work
Transfer of Energy
Relationship to Kinetic Energy 1

2. Conservation of Energy
Energy is “Conserved” meaning it cannot be created nor destroyed!
Energy can change form.
Energy can be transferred.
Total Energy does not change with time.
This is a BIG deal!
Maybe do example of conservation (like cookies) and counter example. Force is NOT conserved.

3. Energy Forms of Energy: Units: Joules (J) = kg-m2/s2
Kinetic Energy (energy of Motion)
Potential Energy (Stored energy)
Heat (later this semester…)
Mass (E=mc2) (in Physics 102)
Units: Joules (J) = kg-m2/s2

4. Work by Constant Force W = F x cos (units: J) F Dx F Dx F Dx
Work can be positive:
Work can be zero:
Work can be negative: F q x Dx F
WF > 0 if 0  q < 90 since cosq > 0 Dx F
WF = 0 if q = 90 since cosq = 0 Dx F
WF < 0 if 90 < q  since cosq < 0

5. Work by Variable Force W = Fx Dx Work is area under F vs. x plot. Work
Spring F = k x (a changing force).
Area = ½ k x2 = Wspring
Force
Work
Distance
Force
Distance
F=kx
Work

6. Kinetic Energy: Motion
Apply constant force along x-direction to a point particle m.
W = Fx Dx
= m ax Dx
= ½ m (v2 – v02)
Work changes ½ m v2
Define Kinetic Energy: K = ½ m v2
Thus: W = D K (For Point Particles)

7. Summary Energy is Conserved Work = transfer of energy using force
Can be positive, negative or zero
W = F x cos(q)
Kinetic Energy (Motion)
K = ½ m v2
Work = Change in Kinetic Energy
Wnet = DK

8. Example: Block w/ friction
A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface?
We will use: Wnet = K
To do this, we need to find expressions for Wnet and K
First: K
Second: Wnet
5 m/s
3 m

9. Example: Block w/ friction
A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface?
K = Kf - K0
= ½ m vf2 – ½ m v02
= 0 – ½ m v02
= – ½ m v02
K = ½ m v2
vf = 0 m/s

10. Example: Block w/ friction
A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface?
WN = 0 since cos90º = 0
Wg = 0 since cos90º = 0
Wf = Ff x cos = -mgd (since cos180º = -1) Fg FN Ff
Wnet = WN + Wf + Wg
= 0 + -mgd + 0
= -mgd x y

11. Example: Block w/ friction
A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface?
Wnet = D K
-mgd = -½ m v02
gd = ½ v02