#### Transcript x F F=kx

```General Physics I: Day 15
Power & Gravitational Potential Energy
Make sure your iClicker is registered at UserID!
Worked-Example: Sailboat
• What is the speed of the
boat after it has travelled
200 m under the action of
this force?
2
Worked-Example: Sailboat
3
Worked-Example: Sailboat
4
Springs & Hooke’s Law
5
Hooke was a contemporary of Newton’s who was
very critical of Newton’s work.
Hooke’s law: A spring exerts a force
that is directly proportional to the
Fsp rin g  k  L
amount by which the spring is
stretched or compressed.
Fsp rin g  kx
If we assume that 𝑥 is measured
relative the relaxed position then
𝑘 is called the spring constant, it measures the
stiffness of the spring in units of N/m.
6
Spring Work
So lets apply our general form for work to find the
b
work done against a spring:
W 
F
ds
a
F=kx
F
x
W o n sp r. 
 dx
kx

0
x
Again 𝑥 is measured from
the relaxed position.
W o n sp r. 
1
2
W by spr.  
kx
1
2
2
kx
2
WarmUp: Kinetic Energy Race
7
Two cars, one four times as heavy as the other, are at
rest on a frictionless horizontal track. Equal forces act
on each of these cars for a distance of exactly 5 m. The
kinetic energy of the lighter car will be _______ the
kinetic energy of the heavier car.
~45% → one-quarter
~11% → one-half
~28% → equal to
~9%
~9%
→ twice
→ four times
8
Two cars, one four times as heavy as the other, are at rest
on a frictionless horizontal track. Equal forces act on each
of these cars for a distance of exactly 5 m. The kinetic
energy of the lighter car will be _______ the kinetic energy
of the heavier car.
A) one-quarter
B) one-half
C) equal to
D) twice
E) four times
9
On Monday you run up the stairs to the top floor of a
tall building, running at constant speed. On Tuesday
you walk to the top, also at constant speed. On
Wednesday you take a constant speed elevator. Call
the work you do to get to the top of the building
𝑊M, 𝑊T and 𝑊W respectively. Rank these works.
A) 𝑊M = 𝑊T = 𝑊W
B) 𝑊M > 𝑊T > 𝑊W
C) 𝑊M = 𝑊T > 𝑊W
D) 𝑊T > 𝑊M = 𝑊W
WarmUp: Sustained Power
10
Some athletes can put out as much as 700
watts in short bursts. Assuming you could
sustain such an energy output for 1 hour(!),
estimate how fast would you be traveling
at the end of that time period.
~25% → Used power → work → kinetic → speed
~8% → Realized they were stuck
~42% → Went ahead with ideas that didn’t work
~25% → Talked a bit, but gave no estimate
WarmUp: Sustained Power
11
“In my exercise physiology class we learned about
the Running Anaerobic Sprint Test that is used to
evaluate power output for runners. I figured the
mass of an athlete to be around 72.6kg The formula
used is Power=(bodymass*distance^2)/time^3.
But then I thought about the Kinetic energy
equation which is K=1/2m*v^2 So, I used
700=1/2*72.6(v)^2 I solved for V and I ended up
with 4.39m”
WarmUp: Sustained Power
“Using P=W/t, with flipping it around to P*t=W
you would get 700watts/hour is the speed of the
runner.”
“watts=power=work/time
work=3600[s]*700[w]=2520000[J]
2520000=.5mv^2 mv^2=5040000
v^2=5040000/94.1kg(usain bolt's mass)=53560
v=231.43m/s (518 mph!!)”
12
WarmUp: Sustained Power
13
“Honestly Im not sure how to answer this question.
I understand that 700 watts equals the power, then 1
hr or 3600 seconds is the time, and my mass is
about 45 kg. And since Work is equal to the change
in kinetic energy, I found my work or KE to be
2.52*10^6, then plugging that into .5*m*v^2, I
found v to be 335 m/s which seems utterly
inhuman....”
14
Power
Notice that time is not part of defining work.
The amount of work it takes to lift your book is
independent of the time the process takes.
But we definitely care…
We define power as the rate at which work is done:
P 
dW
dt
For a microwave, we care about power, not total
work done.
Units of Power
Units for power are watts, named
after James Watt (steam engine!)
Watt coined the term “horsepower”,
(an alternative unit for power).
1 hp = 760 W.
A car engine’s horsepower tells you the rate at
which the engine can do work.
15
16
Power Ratings
Appliances offer a great example comparison
between power and energy.
We care about how much energy each one
transforms (uses) in a given amount of time.
So appliances have power
Appliance Power (W)
ratings in watts. (1 W = 1 J/s) Stovetop
12,000
So each second you use a
hairdryer, it converts 1000 J
of EEM into K and Eth.
Microwave
1,400
Hair Dryer
1,000
TV, color
350
Instantaneous Power
17
As an object moves, the power expended on it
depends on:
• The strength of the force
• How far the object moves
• How much time the movement takes
The result is that we can calculate the instantaneous
power due to a particular force simply with:
P  F v
Potential Energy
18
Associated with certain forces.
Potential energy is associated with a particular
configuration of 2 or more objects (a system).
Reference point:
• When using potential energy you must always define
• Arbitrary (usually), but some choices are easier.
• Regardless of your reference point, the change in
potential energy from one configuration to another
will always be the same!
Conservative vs. Non-Conservative
19
Conservative forces defined in a couple ways:
• Conceptually a conservative force is one which
will “store” energy that can be released later.
• Technically a conservative force is one for which
the work done by that force is independent of the
path taken by the object.
ALL forces conserve energy, but conservative
forces are special… they also conserve mechanical
energy.
Coming up…
Tuesday (10/14) → 7.2 – 7.3
Homework 6 due Sunday by 11:59 PM
Warm-Up due Monday by 10:00 PM
Come pick up Worked-Examples Journal Part II if
you don’t have one yet…
Make sure your iClicker is registered at UserID!
Exam 1…
20
Exam I
Average: 48/80, 60% (middle D on my scale)