Transcript Work and Energy Chapter 6

Chapter 4 Activity 2
GPE and KE
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Potential Energy
Potential Energy: stored energy.
There are many ways that energy can be stored
and then released. It’s a lot like saving money in
the bank so that it can be used later...
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Gravitational Potential Energy
When an object is lifted to a particular height, the
stored energy due to its elevated position
increases. A dam is a good example of this.
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Gravitational Potential Energy Definition
GPE = weight x height
GPE = (mg) h
GPE = mgh
Mass [in kg] multiplied by the acceleration due to
gravity (“g”: 9.8 m/s/s) is the object’s weight.
The units of energy are [Joules].
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GPE Example:
A crane lifts a steel beam
with a mass of 2500 kg to
a height of 20 m. How
much gravitational
potential energy does the
beam have?
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GPE Example
Use the mathematical definition of GPE:
(You may round “g” to 10 m/s/s)
• GPE = (m g) h
• (2500kg * 10 m/s2)* 20 m
• 25,000 N * 20 m
• 500,000 J
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Reference Point, Base Level
When measuring an “h” to calculate GPE, it’s
important to know where you are measuring
from (like the pendulum in lab).
Any point can be used as a base level because the
energy amount you calculate will be relative.
However, you must be consistent.
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Kinetic Energy
Kinetic Energy, KE: energy of motion
KE = 1/2 m v2
m = mass
v = velocity
Any object in motion has kinetic energy.
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Objects with a small mass can have high kinetic
energy if their velocity is high.
(Example: a bullet)
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Objects moving at slow speed can have great
kinetic energy if their mass is great.
(Example: a freighter)
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KE Example:
Ex: A 80 kg sprinter may average about 10 m/s
during a 100m dash. What would his KE be?
KE = 1/2 mv2
KE = 1/2 (80kg) (10m/s)2
KE = 4000 kgm2/s2
KE = 4000 J
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Conservation of Energy:
Energy cannot be created or destroyed; it may be
transformed from one form into another, but the
total amount of energy never changes.
K.E.
P.E.
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For an object that drops, any energy “lost” is
usually released in the form of heat energy due to
friction. In any problems in class, we will assume
that our roller coaster track is “frictionless”.
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At the top, the
diver has all PE
As he falls, PE is
changed to KE.
Before he hits,
all the PE has
changed to KE.
Notice
that the
total
amount of
energy
remains
constant.
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Example:
Question: If a 2 kg brick were to fall from a
building 45 m high, how fast would it be
traveling just before it hits the ground?
2kg
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Solution:
GPEtop = KEbottom
mgh = mv2/2
(2kg) (10m/s2) (45m) = (2kg) v2/2
notice “m” cancels out
(10m/s2) (45m) = v2/2
450 m2/s2 = v2/2
900 m2/s2 = v2
v= 30 m/s
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Graphing of Lab Data
•
•
•
•
•
GPEtop = KEbottom
mgh = mv2/2
gh = v2/2
v2 = (2g) h
If there was no friction, your lab data
should have given you a slope of 19.6 m/s/s
(this is 2g!)
• Which set of lab data was closest?
– Pendulum, Low or High Angle Tracks? 17