Transcript The Nature of Energy

The Nature of Energy
The Nature of Energy

Energy
 The
ability to cause change.
 Scalar quantity.
 Does
 Unit:
NOT depend on direction.
kg*m2/s2
=
N*m
 = Joule (J)

All energy can be broadly classified as
potential or kinetic.
 Potential
energy – energy in storage.
 Kinetic energy – energy in motion.
Forms of Energy

Energy can change from
one form to another.

Remember “I SCREAM”







I = Internal
S = Sound
C = Chemical
R = Radiant
E = Electrical
A = Atomic
M = Mechanical
Forms of Energy

Internal Energy
 energy
assoc. with particles in a substance.
 temperature and phase are assoc. w/ internal
energy.

Sound Energy
 released
when an object vibrates.
 needs a medium in which to travel.
Forms of Energy

Chemical Energy
 Energy
stored in chemical bonds.
 Batteries, gasoline, and food all store
chemical potential energy.

Radiant Energy
 Energy

carried by light.
Electrical Energy
 Energy
assoc. w/ the movement of electrons
through a substance.
Forms of Energy

Atomic Energy
 Energy
stored in the nucleus of an atom
(nuclear energy).

Mechanical Energy
 Kinetic
= energy assoc. with a moving object.
 Potential = energy assoc. with an object b/c
of its position or deformation.
Kinetic Energy (K)

Energy of a moving object.
K
= ½ mv2
Kinetic Energy
Velocity = 5 m/s
Kinetic Energy (J)
1400
1200
1000
800
600
400
200
0
0
20
40
60
Mass (kg)
80
100
Kinetic Energy
Kinetic Energy (J)
Mass = 10 kg
16000
14000
12000
10000
8000
6000
4000
2000
0
0
10
20
30
40
Velocity (m/s)
50
60
Kinetic Energy

What is the kinetic energy of a 1500.-kg
vehicle moving at 20.0 m/s?
K
=
K =
K =
K =
½ mv2
½ (1500. kg)(20.0 m/s)2
½ (1500. kg)(400. m2/s2)
3.00x105 J
Kinetic Energy

A .30-06 bullet has a mass of 11.2 grams
and a kinetic energy of 3840 J. What is
the speed of the bullet?
 First
convert grams to kilograms:
 11.2
K
g = 0.0112 kg
= ½ mv2
 3840 J = ½ (0.0112 kg)v2
 686 000 m2/s2 = v2
 v = 828 m/s
Gravitational Potential Energy

Ug – Energy stored by an object because
of its position in a gravitational field.
 Ug
= mgh
m
= mass (kg)
 g = gravity (m/s2)
 h = height (m)
 Must
always be measured relative to some
point.
Gravitational Potential Energy

As an object falls, Ug turns to K.
 Ug

In a world w/o friction, Mech. Energy is
constant.
K

+ K = Mechanical Energy
+ Ug = constant for all falling bodies
In the real world, friction robs moving
objects of energy
 Mech.
Energy of a free-falling body in Earth’s
atmosphere constantly diminishes.
Mechanical Energy
Ideal World
Ug,o
K=0
K = Ug,o
Real World
Ug,o
K=0
K < UG,o
Mechanical Energy

A 2.00-kg stone is dropped from a height
of 50.0 meters. What is its velocity when
it reaches the ground? (Ignore air
resistance)
 In
the absence of drag, its K upon reaching
the ground = its starting Ug.
 Ug = mgh = (2.00 kg)(9.81 m/s2)(50.0 m)
 Ug = 981 J
 K = 981 J
Mechanical Energy

A 2.00-kg stone is dropped from a height
of 50.0 meters. What is its velocity when
it reaches the ground? (Ignore air
resistance)
K
= 981 J
 981 J = ½ (2.00 kg)v2
 981 J = (1.00 kg)v2
 981 m2/s2 = v2
 v = 31.3 m/s
Mechanical Energy

The Titan roller coaster at Six Flags Over Texas
features a drop of 255 feet (77.7 meters) and
has a top speed of 85 mph (38.0 m/s).
Mechanical Energy

If the mass of a roller coaster train is 5000. kg,
what is the GPE of the train at the top of the
first hill (relative to the bottom of the hill)?


GPE = mgh = (5000. kg)(9.81 m/s2)(77.7 m)
GPE = 3.81x107 J
Ug = 38.1 million Joules
Mechanical Energy

The 5000.-kg train is moving at 38.0 m/s at the
bottom of the first hill. What is the car’s KE?



KE = ½ mv2
KE = ½ (5000. kg)(38.0 m/s)2
KE = 3.61x107 J
Ug = 38.1 million Joules
K = 36.1 million Joules
Mechanical Energy

How much of the car’s Mech. Energy was
converted to other forms in the first drop?


3.81x107 J – 3.61x107 J = 2.0x106 J
What kinds of energy might the mechanical
energy have been converted to?
Ug = 38.1 million Joules
K = 36.1 million Joules
Mechanical Energy

Imagine a 50.0-kg crate perched on shelf
2.0 meters above the ground.
 Now
imagine the same crate on the same
shelf, except now it’s on the Moon.

Does the crate have more, the same, or
less Ug on the Moon than it has on Earth?
has less because g is smaller on the Moon
than it is on Earth.
 It
Elastic Potential Energy

Ue = energy stored by an object when it is
deformed.
 Most

common example: springs
Ue = ½ kx2
k
= spring constant (N/m)
 x = stretch (m)
For You Calculus People
Recall that Fspring = kx.
 If f(x) = ½ kx2, then f’(x) = kx

 In
other words, the force needed to stretch a
spring to a distance x is the first derivative of
the potential energy stored in the spring when
it is stretched to x.
 Also, the potential energy is the integral of a
force-vs-stretch graph.
Elastic Potential Energy
k = 50 N/m
Spring Force (N)
12
10
8
6
4
2
Ue = ½ kx2
0
0
5
10
Stretch (cm)
15
20
Elastic Potential Energy

How much force is required to stretch a
50.0-N/m spring 25.0 cm? How much
potential energy is stored in the stretched
spring?
 Fs
= kx
 Fs = (50.0 N/m)(0.250 m) = 12.5 N
 Ue = ½ kx2
 Ue = ½ (50.0 N/m)(0.250 m)2 = 1.56 J