Transcript 6-7 Problem Solving Using Conservation of

Chapter 6
Work and Energy
Objectives: The student will be
able to:
1. State the law of conservation of energy and
apply the law to problems involving mechanical
energy.
• An object has the MOST kinetic energy when
it’s movement is the GREATEST.
• When an object has the LEAST potential
energy, it has the MOST kinetic energy.
A water bottle is knocked off a desk.
When does the bottle have the MOST
kinetic energy?
A. At the top of the fall.
B. In the middle of the fall.
C. At the bottom of the fall.
• C. At the bottom of the fall.
• It has the most kinetic energy when its movement
and speed are greatest, which is at the bottom of the
fall right before it hits the ground.
• When an object has the LEAST potential energy is
when it has the MOST kinetic energy.
BrainPop
Roller Coasters
• When does the train on
this roller coaster have
the MOST potential
energy?
• AT THE VERY TOP!
• The HIGHER the train is lifted
by the motor, the MORE
potential energy is produced.
• At the top of the hill the train
has a huge amount of potential
energy, but it has very little
kinetic energy.
• As the train accelerates down the hill the
potential energy is converted into kinetic
energy.
• There is very little
potential energy at
the bottom of the
hill, but there is a
great amount of
kinetic energy.
• When does the train
on this roller coaster
have the MOST
kinetic energy?
(When is it moving the fastest?)
(When does it have the LEAST
potential energy???)
• At the bottom of the
tallest hill!
The Conservation of
Mechanical Energy
THE PRINCIPLE OF
CONSERVATION OF
MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an object
remains constant as the object moves, provided that the net
work done by external non-conservative forces is zero.
Conservation of Mechanical Energy
If friction and wind resistance are ignored, a bobsled run
illustrates how kinetic and potential energy can be
interconverted, while the total mechanical energy remains
constant.
6-6 Mechanical Energy and Its
Conservation
If there are no nonconservative forces, the sum
of the changes in the kinetic energy and in the
potential energy is zero – the kinetic and
potential energy changes are equal but opposite
in sign.
This allows us to define the total mechanical
energy:
And its conservation:
(6-12b)
6-7 Problem Solving Using Conservation of
Mechanical Energy
In the image on the left, the total
mechanical energy is:
The energy buckets (right)
show how the energy
moves from all potential to
all kinetic.
6-7 Problem Solving Using Conservation of
Mechanical Energy
If there is no friction, the speed of a roller
coaster will depend only on its height
compared to its starting height.
6-7 Problem Solving Using Conservation of
Mechanical Energy
For an elastic force, conservation of energy tells
us:
(6-14)
Rollercoaster Example
• Loss in height corresponds to a gain in
speed as total energy is conserved.
Skier Example #1
• When the skier loses his total mechanical
energy, work is done on the snow and the
snow gains the energy.
A Daredevil Motorcyclist
A motorcyclist is trying to leap across the
canyon shown in the Figure above by driving
horizontally off the cliff at a speed of 38.0 m/s.
Ignoring air resistance, find the speed with
which the cycle strikes the ground on the
other side.
Roller Coaster (Ideal)
The Magnum XL-200 at Cedar Point Park
In Sandusky, Ohio. The ride includes a
vertical drop that accelerates the cart to a
speed of 34 m/s (76 mi/hr) at the bottom of
the dip. Assume that the coaster has a
speed of nearly zero as it crests the top of
the hill. Neglecting friction and other nonconservative forces, determine the
approximate height of the peak.
Hint: Use the energy approach.
Non-conservative Forces for
the Roller Coaster Example
In the roller coaster example, we ignored
non-conservative forces, such as friction. In
reality, however, such forces are present
when the roller coaster descends.
Energy in a Roller Coaster Ride
1.
2.
3.
4.
5.
6.
Go to the following site:
http://www.pbslearningmedia.org/resource/hew06.sci.phys.maf.rollercoaster/energy-in-aroller-coaster-ride/
Run the animation and observe the relationship between kinetic and potential energy at
each position.
Stop the roller coaster and at each position and describe on a sheet of paper the
relationship between kinetic and potential energy using the pie chart. Then explain in
detail why that relationship exists based on the information given in the animation.
Now you will design your own roller coaster. Go to the following site:
http://www.learner.org/interactives/parkphysics/coaster/
Follow the directions on how to build your roller coaster. Think through each step carefully
and the physics behind each step.
When you are finished you, will get an analysis of your design. On the back of the paper
you used for the previous activity, explain why your steps were successful in terms of
energy or why you were not successful and what needs to be done in order to improve
your design.
Homework Problems Chapter 6
• #33 (first question of 33), 37, 40, 41, 43
Closure
• Kahoot 6-6 and 6-7