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Kinetic and Potential Energy
It’s “Natural Money”
Kinetic and Potential Energy
The sum of K + Ug is known as the total mechanical energy of a
system – in the absence of friction this value does not change
regardless of motion or the path taken by an object.
Energy Bar Charts
 A pebble is tossed up into the air.
 The simple bar charts below show how the sum of K + Ug
remains constant as the pebble rises and then falls.
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Slide 10-34
Energy Bar Charts
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Conservation of Energy
Energy is neither created nor destroyed only changed from one form to another
To problem solve using conservation of energy use Energy initial = Energy final
*identify what type of energy is present initially
*identify what type of energy is present at the end point
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QuickCheck 10.5
Starting from rest, a marble
first rolls down a steeper hill,
then down a less steep hill of
the same height. For which is
it going faster at the bottom?
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A.
Faster at the bottom of the steeper hill.
B.
Faster at the bottom of the less steep hill.
C.
Same speed at the bottom of both hills.
D.
Can’t say without knowing the mass of the marble.
Slide 10-49
QuickCheck 10.5
Starting from rest, a marble
first rolls down a steeper hill,
then down a less steep hill of
the same height. For which is
it going faster at the bottom?
© 2013 Pearson Education, Inc.
A.
Faster at the bottom of the steeper hill.
B.
Faster at the bottom of the less steep hill.
C.
Same speed at the bottom of both hills.
D.
Can’t say without knowing the mass of the marble.
Slide 10-50
QuickCheck 10.7
Three balls are thrown from
a cliff with the same speed
but at different angles.
Which ball has the greatest
speed just before it hits the
ground?
© 2013 Pearson Education, Inc.
A.
Ball A.
B.
Ball B.
C.
Ball C.
D.
All balls have the same speed.
Slide 10-57
QuickCheck 10.7
Three balls are thrown from
a cliff with the same speed
but at different angles.
Which ball has the greatest
speed just before it hits the
ground?
© 2013 Pearson Education, Inc.
A.
Ball A.
B.
Ball B.
C.
Ball C.
D.
All balls have the same speed.
Slide 10-58
FRQ Practice
A roller coaster car of mass m = 200 kg is released from rest at the top of a 60 m high hill
(position A) and rolls with negligible friction down the hill, through a circular loop of radius 20 m
(positions B, C, and D), and along a horizontal track ( to position E).
(a) What is the velocity of the car at position B?
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b. Determine the velocity of the car at position C
c. Draw free-body diagram of the car at position C
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d. Determine the velocity of the car at position D
e. Determine the Force (magnitude and direction) of the track on the car at position D
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After completing the loop, the roller coaster car is traveling horizontally at velocity v o and subjected
to a braking force Fbraking = -kv, where k is a constant, v is the instantaneous velocity of the car, and
time t is the amount of time that the braking force has been applied
i. Develop a definite integral-expressed in terms of initial velocity vo, k, m, and time t that could be
used to evaluate the velocity of the car along the horizontal track
ii.
Solve the integral to determine an equation that could be used to calculate the horizontal
velocity of the car as a function of initial velocity vo, k, m, and time t.
© 2013 Pearson Education, Inc.