Transcript Welcome to PHY 1151: Principles of Physics I

Chapter 8
Potential Energy and Conservation
of Energy
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Department of Physics
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Outline
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Gravitational Potential Energy
Conservation of Mechanical Energy
Examples
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Gravitational Potential Energy
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Gravitational potential energy
U: The energy of a body due to
elevated positions is called
gravitational potential energy.
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U = weight  height = mgh
The gravitational potential energy is
relative to the reference level and
depends only on mg and the height h.
Work done by a conservative force
is equal to the negative of the
change in potential energy.
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Wc = - U = - (Uf – Ui) = Ui - Uf
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Example 1
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Find the gravitational
potential energy of a 65-kg
person on a 3.0-m-high
diving board. Let U = 0 be
at water level.
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Department of Physics
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Example 2
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An 82.0-kg mountain
climber is in the final
stage of the ascent of
4301-m-high Pikes Peak.
What is the change in
gravitational potential
energy as the climber
gains the last 100.0 m of
altitude? Let U = 0 be (a)
at sea level and (b) at the
top of the peak.
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Conservation of Mechanical
Energy
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Mechanical energy E: The
sum of the potential and
kinetic energy of an object.
E = U + K.
Conservation of
mechanical energy: In
systems with conservative
forces (such as gravity) only,
the mechanical energy E is
conserved. Ui + Ki = Uf + Kf.
Dr. Jie Zou PHY 1151G
Department of Physics
Assume
there is no
air
resistance.
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Conservation of Energy
Mechanical Ei
= 100 J
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When Friction
exists
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Mechanical Ef
= 90 J
Decrease in mechanical
energy = Ei – Ef = 10 J =
Thermal energy converted
Energy cannot be created or
destroyed; it may be
transformed from one form
into another, but the total
amount of energy never
changes.
The universe, in short, has a
certain amount of energy, and
that energy simply ebbs and
flows from one form to
another, with the total amount
remaining fixed.
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Example 1
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A player hits a 0.15-kg
baseball over the outfield
fence. The ball leaves the
bat with a speed of 36 m/s,
and a fan in the bleachers
catches it 7.2 m above the
point where it was hit.
Assuming frictional forces
can be ignored, find (a) the
kinetic energy of the ball
when it is caught and (b)
its speed when caught.
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Example 2
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A 55-kg skateboarder
enters a ramp moving
horizontally with a
speed of 6.5 m/s, and
leaves the ramp
moving vertically with
a speed of 4.1 m/s.
Find the height of the
ramp, assuming no
energy loss to
frictional forces.
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Example 3
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d=?
If the height of the water
slide is h=3.2 m, and the
person’s initial speed at
point A is 0.54 m/s, what
is the horizontal distance
between the base of the
slide and the splashdown
point of the person?
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Example 4
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Suppose the pendulum bob
has a mass of 0.33 kg and is
moving to the right at point B
with a speed of 2.4 m/s. Air
resistance is negligible.
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(a) What is the change in the
system’s gravitational potential
energy when the bob reaches
point A?
(b) What is the speed of the
bob at point A?
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Potential Energy of a Spring
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U = (1/2)kx2
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k = the force constant (N/m) of
the spring
x = the displacement of the
spring from its equilibrium
position
Example: If k = 680 N/m and
x = 2.25 cm, then U =
(1/2)(680 N/m)(0.0225 m)2 =
0.172 J
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Example
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Experiments performed on the wing
of a hawkmoth show that it deflects
by a distance of x = 4.8 mm when
a force of magnitude F = 3.0 mN is
applied at the tip. Treating the wing
as an ideal spring, find
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(a) the force constant of the wing
(b) the energy stored in the wing
when it is deflected
(c) what force must be applied to the
tip of the wing to store twice the
energy found in part (b)?
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Homework
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See online homework assignment at
www.masteringphysics.com
Hand-written homework assignment:
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Chapter 8, Page 247-250, Problems: #34,
86.
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Department of Physics
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