Download Conservation of Energy

Conservation of Mechanical
Energy
What do you think?
• Imagine two students standing side by
side at the top of a water slide. One steps
off of the platform, falling directly into the
water below. The other student goes down
the slide. Assuming the slide is frictionless,
which student strikes the water with a
greater speed?
– Explain your reasoning.
• Would your answer change if the slide
were not frictionless? If so, how?
What do you think?
• What is meant when scientists
say a quantity is conserved?
• Describe examples of quantities
that are conserved.
–Are they always conserved? If not,
why?
Mechanical Energy (ME)
ME = KE + PEg + PEelastic
Elastic
Energy
Gravitational
1 Kinetic
1 2
2
KE  mv
PE elastic  kx
Potential
Potential2
2
PE gravity
Hooke’s Law
Energy
Energy
 mgh
Mechanical Energy (ME)
• ME = KE + PEg + PEelastic
–Does not include the many other
types of energy, such as thermal
energy, chemical potential energy,
and others
• ME is not a new form of energy.
–Just a combination of KE and PE
Classroom Practice Problems
• A 1.00 kg book is dropped from
a height of 2.00 m. Assume no
air resistance.
–Calculate the PE and the KE at
the instant the book is released.
• Answer: PE = 19.6 J, KE = 0 J
Classroom Practice Problems
• A 1.00 kg book is dropped from a
height of 2.00 m. Assume no air
resistance.
–Calculate the KE and PE when the
book has fallen 1.0 m. (Hint: you will
need an equation from Chapter 2.)
• Answer: PE = 9.81 J, KE = 9.81 J
Classroom Practice Problems
• A 1.00 kg book is dropped from a
height of 2.00 m. Assume no air
resistance.
–Calculate the KE and PE just before
the book hits the ground
• Answer: PE = 0 J, KE = 19.6 J
Table of Values for the Falling
Book
h (m)
PE(J)
KE(J)
ME(J)
0
19.6
0
19.6
0.5
14.7
4.9
19.6
1.0
9.8
9.8
19.6
1.5
4.9
14.7
19.6
2.0
0
19.6
19.6
Conservation of Mechanical
Energy
MEi = MEf
Initial ME = Final ME
• The sum of KE and PE remains constant.
• One type of energy changes into another type.
– For the falling book, the PE of the book changed into
KE as it fell.
– As a ball rolls up a hill, KE is changed into PE.
PEmax = mgh
KE = 0
PE = mgh
PE + KE = PEmax
PE = mgh
PE + KE = PEmax
PE = 0
KE = PEmax
Conservation of Energy
• Acceleration does not have to be
constant.
• ME is not conserved if friction is
present.
–If friction is negligible, conservation
of ME is reasonably accurate.
• A pendulum as it swings back and
forth a few times
Conservation of Energy
• Consider a child going down a slide
with friction.
–What happens to the ME as he slides
down?
• Answer: It is not conserved but, instead,
becomes less and less.
–What happens to the “lost” energy?
• Answer: It is converted into
nonmechanical energy (thermal energy).
Classroom Practice Problems
• A small 10.0 g ball is held to a
slingshot that is stretched 6.0 cm.
The spring constant is 2.0  102
N/m.
–What is the elastic potential energy
of the slingshot before release?
Ans: 0.36 J
Classroom Practice Problems
• A small 10.0 g ball is held to a
slingshot that is stretched 6.0 cm.
The spring constant is 2.0  102
N/m.
–What is the kinetic energy of the
ball right after the slingshot is
released?
Ans: 0.36 J
Classroom Practice Problems
• A small 10.0 g ball is held to a
slingshot that is stretched 6.0 cm.
The spring constant is 2.0  102
N/m.
–What is the ball’s speed at the
instant it leaves the slingshot?
Ans: 8.5 m/s
Classroom Practice Problems
• A small 10.0 g ball is held to a
slingshot that is stretched 6.0 cm.
The spring constant is 2.0  102
N/m.
–How high does the ball rise if it is
shot directly upward?
Ans: 3.7 m
Problem Solving Process
• Draw a sketch
• Identify: KEi, PEi, KEf, and PEf
–Include both gravitational and
elastic PE, as needed
• Apply the equation:
(KE + PE)i = (KE + PE)f
• Solve for required quantity
–Mass, speed, distance, height, etc.
Practice Problem
• Starting from rest, a child zooms down a
frictionless slide from an initial height of
3.00m. What is her speed at the bottom of
the slide? Assume she has a mass of 25.0
kg.
Nonconservative Forces
with Energy Considerations


When nonconservative forces are
present, the total mechanical energy of
the system is not constant
The work done by all nonconservative
forces acting on parts of a system
equals the change in the mechanical
energy of the system

Wnc  Energy
Nonconservative Forces
and Energy

In equation form:
Wnc   KEf  KEi   (PEi  PEf ) or
Wnc  (KEf  PEf )  (KEi  PEi )

The energy can either cross a boundary
or the energy is transformed into a
form of non-mechanical energy such as
thermal energy
Transferring Energy

By Work


By applying a
force
Produces a
displacement of
the system
Transferring Energy

Heat


The process of
transferring heat by
collisions between
molecules
For example, the
spoon becomes hot
because some of the
KE of the molecules in
the coffee is
transferred to the
molecules of the
spoon as internal
energy
Transferring Energy

Mechanical Waves


A disturbance
propagates
through a medium
Examples include
sound, water,
seismic
Transferring Energy

Electrical
transmission


Transfer by means
of electrical
current
This is how energy
enters any
electrical device
Transferring Energy

Electromagnetic
radiation

Any form of
electromagnetic
waves

Light, microwaves,
radio waves
Notes About Conservation
of Energy

We can neither create nor destroy
energy



Another way of saying energy is
conserved
If the total energy of the system does
not remain constant, the energy must
have crossed the boundary by some
mechanism
Applies to areas other than physics
Now what do you think?
• Imagine two students standing side by
side at the top of a water slide. One steps
off of the platform, falling directly into the
water below. The other student goes down
the slide. Assuming the slide is frictionless,
which student strikes the water with a
greater speed?
– Explain your reasoning.
• Would your answer change if the slide
were not frictionless? If so, how?
Now what do you think?
• What is meant when scientists say a
quantity is “conserved”?
• Describe examples of quantities that are
conserved.
– Are they always conserved? If not, why?