Download PHYS 1114: Physics I

PHYS 1114: Physics I
An Overview of Energy
• Energy is conserved.
Lecture 6:
Conservation of Energy
• Kinetic Energy describes motion and relates to the mass of
the object and it’s velocity squared.
• Energy on earth originates from the sun.
• Energy on earth is stored thermally and chemically.
• Chemical energy is released by metabolism.
Professor Kenny L. Tapp
• Energy is stored as potential energy in object height and
mass and also through elastic deformation.
• Energy can be dissipated as heat and noise.
Energy Stored thru Elastic Deformation...
A Close Look at Energy Transformation...
• This transformation begins as
elastic potential energy in the
elastomer.
•It then becomes kinetic energy
as the projectile flies upward.
•During the upward flight,
kinetic energy becomes
potential until at the top of the
flight, all the energy is
potential.
• Finally, the stored potential
energy changes back to kinetic
energy as the projectile falls.
Kinetic Energy
Kinetic energy is defined as:
The net work on an object changes its kinetic energy.
Kinetic Energy
This relationship is called the work–energy theorem.
Quick Question 1:
Potential Energy
Gravitational potential energy:
Determine which car has the most and least amount of
Kinetic Energy.
Potential Energy of a Spring
We can, therefore, define the potential energy of a spring; note
that, as the displacement is squared, this expression is
applicable for both compressed and stretched springs.
Quick Question 2:
A 10.0 kg object is moved from the 2nd floor of a
house 3.00 m above the ground to the first floor
0.30 m above the ground.
What is the change in gravitational potential energy?
U = mgy
Potential Energy
Only changes in potential energy are physically significant;
therefore, the point where U = 0 may be chosen for convenience.
Conservation of Energy
Conservation of Energy
Conservation of Energy
We observe that, once all forms of energy are accounted for, the total energy of
an isolated system does not change. This is the law of conservation of energy:
The total energy of an isolated system is always conserved.
We define a conservative force:
A force is said to be conservative if the work done by it
in moving an object is independent of the object’s path.
Conservation of Energy
Conservation of Energy
Another way of describing a conservative force:
A force is conservative if the work done by it in
moving an object through a round trip is zero.
For a conservative force:
We define the total mechanical energy:
Many kinematics problems are much easier to solve using energy conservation.
Einitial = Efinal
Conservation of Energy
Conservation of Energy
All three of these balls
have the same initial
kinetic energy; as the
change in potential
energy is also the same
for all three, their
speeds just before they
hit the bottom are the
same as well.
In a conservative
system, the total
mechanical energy
does not change, but
the split between
kinetic and potential
energy does.
Quick Question 3:
Quick Question 4:
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the greater
speed at the bottom of its ramp?
1
2
3
4) same speed
for all balls
A truck, initially at rest, rolls down a frictionless hill and attains a
speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the
bottom, how many times higher must the hill be?
1) half the height
2) the same height
3) √ 2 times the height
All of the balls have the same initial gravitational PE, since they
are all at the same height (PE = mgh). Thus, when they get to
the bottom, they all have the same final KE, and hence the same
speed (KE = 1/2 mv2).
Quick Question 5:
4) twice the height
5) four times the height
Use energy conservation:
 initial energy: Ei = PEg = mgH
 final energy: Ef = KE = 1/2 mv2
Conservation of Energy:
Ei = mgH = Ef = 1/2 mv2
therefore:
gH = 1/2 v2
So if v doubles, H quadruples!
Quick Question 6:
A 70 kg skier starts from rest on top of 25 m high slope.
What is the speed of the skier at the bottom of the slope?
Neglect friction.
Given the initial velocity of the sledder, how does this
scenario play out? Neglect friction.