Energy Conservation

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Energy Conservation

• And Non-Conservative Forces

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Conservation of Mechanical Energy
Definition of mechanical energy
(8-6)
Using this definition and considering only
conservative forces, we find
Or equivalently
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Conservation of Mechanical Energy
Energy conservation can make kinematics problems
much easier to solve
4
Catching a Home Run
At the bottom of the 9th inning,a player hits a
0.15 kg baseball overthe outfield fence. The
ball leaves the bat with a speed of 36.0 m/sand
a fan in the bleachers catchesit 7.2 m above the
point where itwas hit. Neglect air
resistance. (a) What is the kinetic energy Kf of
the ball when caught? (b) What is the speed vf
of the ball when caught.
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Speed and Path
Energy is a scalar. The speed of the cap is vi
at height yi and its speed is vf at height yf,
independent of the path between the two
heights. Thus the angle at which the cap is
launched does not change this result, as long as
vi is large enough to carry the cap to height yf.
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Energy of a Ball ACT
When a ball of mass m is dropped from height h,
its kinetic energy just before landing is K. If a
2nd ball of mass 2m is dropped from height h/2,
what is its kinetic energy just before landing?
(a) K/4 (b) K/2 (c) K (d) 2K
(e) 4K
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Non-conservative Forces
In the presence of non-conservative forces, the
work done by these forces must be included in the
energy calculations.
This term is equal to the energy expended in
overcoming the non-conservative force (usually
friction) or to the energy gained from work done
by the non-conservative force.
Enc -Wnc
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Skiing w/ Friction
A 50 kg skier goes down a 78 meter high hill with
a variety of slopes. She finally stops at the
bottom of the hill. If friction is the force
responsible for her stopping, how much work does
it do?
0
0
0
Similar to bob sled homework
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Galileos Pendulum ACT

• How high will the pendulum swing on the other
  side now?
• A) h1 gt h2 B) h1 h2 C) h1 lt h2

Conservation of Energy (Wnc0) Kinitial
Uinitial KfinalUfinal 0 mgh1 0 mgh2
h1 h2
m
h1
h2
44
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Find the Divers Depth
A 95.0 kg diver steps off a diving board and
drops into the water, 3.00 m below. At some
depth d below the waters surface, the diver
comes to rest. If the non-conservative work done
on the diver is Wnc -5,120 J, what is the depth
d?
0
0 of U
0
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Judging a Putt
A golfer badly misjudges a putt, giving the ball
an initial speed v1, which sends the ball a
distance d that is only one quarter of the
distance to the hole. If the non-conservative
force f due to the resistance of the grass is
constant, what initial speed v2 would have been
needed to putt the ball from its initial position
to the hole?
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Landing with a Thud
A block of mass m1 2.40 kg is on a horizontal
table with a coefficient of friction mk 0.450
between them and is connected to a hanging block
of mass m2 1.80 kg as shown. When the blocks
are released, they move a distance d 0.50 m,
and then m2 hits the floor. Find the speed of the
blocks just before m2 hits.
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Potential Energy Curvesand Equipotentials
The curve of a hill or a roller coaster is itself
essentially a plot of the gravitational potential
energy
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Potential Energy Curves
The potential energy curve for a mass and spring