Download Lecture 21

Quiz
B
A stone of mass m is thrown straight
upward with an initial velocity V0. Find
the change in gravitational potential
energy (ΔPEg) of the stone between
points
V0
A m
C
a) A and B (PEgB – PEgA) = mgh
b) B and C (PEgB – PEgC) = - mgh
c) A and C (PEgC – PEgA) = 0
Gravitational Potential
Energy PEg
Spring Potential
Energy PEs
Kinetic Energy KE
Energy
ΔKE = W
Kinetic Energy KE
Mass
Velocity
F=constant
F=Mass × Acceleration
2aΔx=vf2 – vi2
2ad=vf2 – vi2
F
0
d
KEf – KEi = Fd
Fdcosθ
KEf – KEi = mad
KEf – KEi = ½ m(vf2 – vi2)
KEf = ½ mvf2
Kinetic Energy KE
KE = ½ mv2
Zero Kinetic Energy?
Depends on a frame of reference!!
Negative Kinetic Energy?
Never!!
final
h
A stone of mass m is thrown straight
upward with an initial velocity V0. Find
the change
a) in gravitational potential energy (ΔPEg)
of the stone
b) in kinetic energy (ΔKE)
c) In total energy, potential + kinetic (ΔE)
Kinematics:
h = V02 /2g
ΔPEg = PEgf – PEgi = mgh – 0
ΔKE = KEf – KEi = 0 – ½ mV02
V0
initial
m
0
ΔE = Ef – Ei = 0
initial
h
m
A stone of mass m is dropped from height
h. Find the change
a) in gravitational potential energy (ΔPEg)
of the stone
b) in kinetic energy (ΔKE)
c) in total energy, potential + kinetic (ΔE)
Kinematics:
h = Vf2 /2g
ΔPEg = PEgf – PEgi = 0 – mgh
ΔKE = KEf – KEi = ½ mV02 – 0
final
Vf
0
ΔE = Ef – Ei = 0
Work-Energy representation
Energy Bar charts
A bar represents each type of
energy in the system:
initial and final.
There is a bar to represent
work done by external objects
on the system.
The work bar is shaded to
indicate that it is not a type of
energy but is a process
involving an interaction
between a system and an
object outside the system.
After
Before
KEi PEgi PEsi
+
0
-
W
KEf PEgf PEsf
1. Define a system
2. Define the initial and final states
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
Before
ΔE = W
KEi PEgi PEsi
+
0
-
W
After
KEf PEgf PEsf
1. Define a system
2. Define the initial and final states
Friction
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
Before
V0
stop
μk
μs
X-?
ΔE = W
KEi PEgi PEsi
+
0
-
W
After
KEf PEgf PEsf
1. Define a system
Pendulum
2. Define the initial and final states
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
Before
ΔE = W
KEi PEgi PEsi
+
1
3
2
0
-
W
After
KEf PEgf PEsf
1. Define a system
2. Define the initial and final states
Roller Coaster
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
Before
ΔE = W
KEi PEgi PEsi
+
0
-
W
After
KEf PEgf PEsf
A: Yes
B: No
C: Need more
information
A hockey puck slides without friction
along a frozen lake toward an ice
ramp and plateau as shown. The
speed of the puck is 4m/s and the
height of the plateau is 1m. Will the
puck make it all the way up the
ramp?
v = 4 m/s
h = 1m
Homework
Due Friday
Read 5.1, 5.2, 5.3, Examples!!!
MC 5, 6, 7, 10
Problems # 8, 25, 30, 41, 43, 46
Quiz
A hockey puck slides without friction
along a frozen lake toward an ice
ramp and plateau as shown. The
height of the plateau is 2m. With
what speed should the puck slide to
make it all the way up the ramp?
V–?
h = 2m