Transcript Document

General Physics I: Day 16
Elastic Potential Energy & Nonconservative Forces
Conservative Forces & Potential Energy
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Conservative forces can “store” energy. Technically
defined in terms of “path-independent” work.
ALL forces conserve energy. Conservative forces
also conserve mechanical energy.
Potential energy:
• Only associated with conservative forces
• Potential energy is associated with a system
• Depends on an arbitrary (usually) reference point
WarmUp: Gravity vs. Friction
A trunk of mass m is lifted along a curved path of length L
to a height h. Another trunk with twice the mass is slid
across a level floor (𝜇𝑘 = 0.5) along a curved path also
having length L. Which is greater, the work done against
friction or the work done against gravity?
~51% → More work is done against friction.
~27% → More work is done against gravity.
~16% → The work done against friction is the same as
the work done against gravity.
~6%
→ Cannot be determined from the given
information.
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Calculating Potential Energy
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For conservative forces, potential energy equals
how much work must be done against that force to
achieve a certain configuration.
 U fo r a fo rce  W d o n e ag ain st fo rce   W d o n e b y fo r ce
For gravity, to move an object from yi to yf:
W ag ain st g rav.  m g  y
o r, if y i = 0
W ag ain st g rav.  m g y
Thus, gravitational potential energy:
U g  m gy
Cons. of Mech. Energy (Gravity only)
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We define mechanical energy: E m ech .  U  K
For an isolated system with only conservative
forces, the total mechanical energy cannot change!
This means that any potential energy gained comes
from kinetic energy lost, and vice versa.
U  K
or
E m ech ., in itial  E m ech ., fin al
or
Ui  Ki  U
f
K
f
Applying Conservation of Mech. Energy
If you decide to use conservation of energy (or of
mechanical energy) you must
• Choose your system!
• Decide on initial and final situations
– One should be as simple as possible, or should
be one you know a lot about
– The other should be what you are trying to
learn about
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Warm-Up: Work & PE
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You throw a ball straight up in the air. On its way
up is the work done by gravity positive or negative?
Is the change in potential energy positive or
negative during this same period?
~10% → Positive W, negative ΔUg
~0% → Positive W, positive ΔUg
~65% → Negative W, positive ΔUg
~15% → Negative W, negative ΔUg
Warm-Up: Work & PE
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“Potential energy is positive, the higher something
is the more kinetic energy that can be produced The
work is negative, due to the fact that the force of
gravity is opposing the current motion of the ball”
Some missed the word “change”!
Warm-Up: Work & PE
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“The work done by gravity is negative, that is
because the work is done in the opposite direction
of motion. The change in potential energy is
positive, because the gravitational potential energy
of the ball increases as the height increases.”
“The change in potential energy is positive but
since work= -change in potential energy. Work done
by gravity is negative.”
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Two marbles, one twice as heavy as the other, are
dropped to the ground from the roof of a building. Just
before hitting the ground, the heavier marble has
A) as much kinetic energy as the lighter one.
B) twice as much kinetic energy as the lighter one.
C) half as much kinetic energy as the lighter one.
D) four times as much kinetic energy as the lighter one.
E) Cannot be determined from what is given.
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A coconut is thrown at a speed of 8 m/s from the top of a
coconut tree and lands on the ground. Rank the following
directions in order of which will result in the largest speed
when the coconut hits the ground.
1) Almost straight up
2) 45° above horizontal
3) Horizontal
4) 45° below horizontal
5) Straight down
A) 1 > 2 > 3 > 4 > 5
B) 1 = 5 > 2 = 4 > 3
C) 1 = 2 = 3 = 4 = 5
D) 5 > 4 > 3 > 2 > 1
Energy: The easy way!
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A block slides down a frictionless ramp, starting out
1.5 meters above the ground (height).
How fast is it going at the bottom of the ramp?
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Two balls will be released from rest at the top of the
apparatus shown. Ball 1 travels on the straight track, while
ball 2 travels on the bent track. If we measure the speed of
each ball as it leaves the track, what will we find?
A) Ball 1 will have a larger final speed.
B) Ball 2 will have a larger final speed.
C) They will have the same final speed.
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Two balls will be released from rest at the top of the
apparatus shown. Ball 1 travels on the straight track, while
ball 2 travels on the bent track. If they are released at the
same time, which ball will reach the end first?
A) Ball 1 will win the race!
B) Ball 2 will win the race!
C) They will tie!
Sample Problem
A Hot Wheels car will roll down a track as shown
on the board. Assume there is no friction in the
motion. From what height should the car be
released so that it is going 0.8 m/s when it reaches
point B which is 11 cm above the bottom of the
track?
An aside: On a homework question you have to
figure out how fast something must go to make it
through a loop-the-loop…
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Worked-Example: Spring Ball Launch
A vertical spring with a spring constant k = 150
N/m is compressed down 1.5 m. A 2-kg ball is
placed on the compressed spring and released
from rest. What height does the ball reach after it
is released?
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Worked-Example: Spring Ball Launch
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Worked-Example: Spring Ball Launch
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Worked-Example: Spring Ball Launch
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Elastic Potential Energy
F
F=kx
W by spr.  
1
2
kx
2
x
Since  U fo r a fo rce  W d o n e b y th at fo rce
U sp rin g 
1
2
Where x is measured from the relaxed position.
kx
2
Difficult/Interesting
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“I thought it was interesting that unlike
gravitational potential energy, for elastic potential
energy we can't just choose x to be 0. It has to be at
the point where the spring is neither compressing or
stretching.”
Cons. of Mech. Energy (Grav. + Elast.)
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We define mechanical energy: E m ech .  U  K
For an isolated system with only conservative
forces, the total mechanical energy cannot change!
This means that any potential energy gained comes
from kinetic energy lost, and vice versa.
U  K
or
E m ech ., in itial  E m ech ., fin al
or
Ui  Ki  U
f
K
f
Sample Problem
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A block (m = 4.5 kg) slides, from rest, down a 12
meter frictionless ramp, which is angled at 30°
above the horizontal. The block then slides along a
frictionless level surface until it encounters a spring
(k = 220 N/m) whose other end is attached to a
wall. What is the maximum distance that the spring
will be compressed by?
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A 2.0 kg block is moving at 10 m/s along a
horizontal frictionless table. It encounters and
compresses a spring whose other end is attached to
a wall. How much potential energy is stored in the
spring at the moment when the block stops moving?
A) 10 J
B) 20 J
C) 100 J
D) Not enough information
Coming up…
Thursday (10/16) → 7.4 – 7.5
Chapter 7 Homework due Sunday by 11:59 PM
Warm-Up due Wednesday by 10:00 PM
In-progress grades are posted!
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