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Work Energy Theorem,
Power,
and Efficiency
Physics 11
Conservation of Energy
 The total energy of a closed system is
constant.
 The total energy in the system is the
sum of the kinetic and potential
energy of it’s various parts.
EKi  EPi  EKf  EPf
Examples
E Ki  EGi  E Kf  EGf
 Book Drop
0  mghi  12 mv 2f  0
h
v
E Ki  ESi  E Kf  ESf
 Collision into a spring
v
1
2
x
mvi2  0  0  12 kx2f
 Car coasting up a hill EKi  EGi  EKf  EGf
v
v
h
1
2
mvi2  0  12 mv 2f  mgh f
Energy is a “State Function”
 Each type/form of energy we have seen so
far is a ‘state function’
 A state function only cares about the
current state of the closed system
 How the system got into that state does not
matter
m
h
All Paths result in the same final velocity
v
Consider the following situation
m
h
r
k
a) What is the velocity at the top of the
loop?
b) What is the maximum compression
of the spring?
Consider the following situation
m
h
r
k
a) What is the velocity at the top of the
loop?
E Ki  EGi  E Kf  EGf
0  mghi  12 mv 2f  0
Consider the following situation
m
r
k
a) b
b) What is the maximum compression
of the spring?
EKi  EGi  ESi  EKf  EGf  ESf
0  mghi  0  0  0  12 kx2f
Check Your Understanding
 A roller coaster starts at a height of
10.0m above the ground with an
initial velocity of 0.50m/s. Determine
the speed at the following points:




5.0m;
7.5m;
2.5m;
At the ground.
Check Your Understanding
 A spring with a spring constant of
550N/m is compressed by 2.5cm and
is used to launch a ball with mass of
75g. Determine:
 The speed of the ball as it leaves the
spring;
 The maximum height the ball attains;
 The ball’s speed when it is 15cm above
its starting point
Rate of Change in Energy
m
h
All Paths result in the same final velocity
v
 So what is different about each of these
paths?
 The time it takes to go down the longer ramp
will be greater due to a lower acceleration
 Power:
W E
P

t t
J 
 s   W 
Efficiency
 Not all systems are closed.
 Energy lost through friction
 Efficiency of energy conversion in
open systems.
Eout
Efficiency 
100%
Ein
Efficiency 
Ef
Ei
100%
Efficiency
 Consider the following:
 A rocket has 3.50x103 J of chemical
potential energy. The stored chemical
energy is transformed into gravitational
potential energy when it is launched.
What is the efficiency of the rocket’s
transformation of energy if the 0.500kg
rocket travels 1.00x102 m.
Practice Problems
Power, Efficiency
 Page 266
 41-43
 Page 270
 44-50
 Page 271
 1-3
Chapter 6 Review
 Page 274