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Work and energy
http://antwrp.gsfc.nasa.gov/apod/
1-D motion
x2
W   Fx dx
Definition of work:
x1
Kinetic energy:
1
2
K  mV
2
Work-energy theorem:
x2
Wtotal   F
net
x
x1
2
2
2
1
mV
mV
dx 

2
2
SI units of work and energy: Joule = Nm=kg m2/s2
James Prescott Joule
b. Dec. 24, 1818, Salford, Lancashire, England
d. Oct. 11, 1889, Sale, Cheshire
Discovered some basic laws of electricity and
thermodynamics (Joule’s Law and JouleThomson Law); established the basis of the
Law of Conservation of Energy and The
First Law of Thermodynamics
Main occupation and source of funding:
Brewery
Was home-schooled by some of the finest scientists of
his time (including John Dalton)
Since childhood, he was a fearless and meticulous experimenter
As a boy, he hiked in the mountains with a pistol, studying echo and the
speed of sound.
He sounded the depth of Lake Windermere to be 198 ft.
He tortured servants with crazy experiments.
Spent his honeymoon climbing in French Alps and measuring the
temperature at the top and the bottom of waterfalls
As a teenager, Joule was trying to replace steam engines
with electric engines in his brewery.
He failed, but became interested in the connections
between mechanical work, heat, and electricity.
In 1840, at the age of 21, he discovered “Joule’s Law”:
Heat generated in a wire
= Resistance x Current^2
It showed that electricity can be converted into heat!
1843 (Age 24): Paddle-wheel experiment: mechanical
work can be converted into heat!
Therefore, heat is one of the forms of energy.
It led to the First Law of Thermodynamics
It also showed that energy is conserved.
Energy Conservation Law!
Met with hostility and disbelief.
It took decades before Joule’s
discovery was accepted.
Only one person believed Joule. It was William Thomson (later
Lord Kelvin). They started working together.
Joule's paper ``On the Mechanical Equivalent of Heat'' was
communicated by Faraday to the Royal Society in 1849 and appeared
in Philosophical Transactions in 1850. The last paragraph of this
historic paper ends with the statements:
I will therefore conclude by considering it as demonstrated by the
experiments contained in this paper:
1.That the quantity of heat produced by the friction of bodies, whether solid
or liquid, is always proportional to the quantity of force extended.
2.That the quantity of heat capable of increasing the temperature of a pound
of water (weighed in vacuo, and taken between 55 deg and 60 deg F) by 1
deg F requires for its evolution the expenditure of a mechanical force
represented by the fall of 772 lb. through a space of one foot.
A third proposition, suppressed by the publication committee, state
that friction consists of a conversion between mechanical work into
heat.
2 or 3 D motion
Definition of work:
 
W   F dr
L
Kinetic energy:
 2
2
2
2
mV
mVx
m |V |
mVz
y



2
2
2
2
Work-energy theorem:
  mV22 mV12
F
d
r


net
L
2
2
A car is stopped by a constant friction force that is
independent of the car’s speed. By what factor is the
stopping distance changed if the car’s initial speed is
doubled?
A person carries a bag of groceries of mass M
with a constant velocity at the same height from
the ground. Find the work done by a person on a
bag.
What if a person drops the bag to the floor from height
1 m with a constant velocity? With a constant
acceleration a?
M
A person is pulling a crate of mass M along the floor with a constant force F over a
distance d. The coefficient of friction is .
(a) Find the work done by the force F on the crate.
(b) Same if F changes as F0(1+x2/d2).
(c) Find the work done by the force of friction on the crate.
(d) Find the net work done on the crate if the crate is pulled with a constant
velocity.
(e) Find the final velocity of the crate if the crate is pulled with a non-zero
acceleration starting from the rest.
Find the work done by a person on a backpack if
(a)A person ascends with a constant speed;
(b) his velocity drops from 3 m/s at the bottom to 0.5 m/s at the top


Hooke' s Law : F  k ( x  x0 )i
x0 is unstreched position
x
Robert Hooke 1635-1703
No portrait survived
(destroyed by Newton??)
Elasticity
Microscopy; first to see cell and name it
Law of gravity ~ 1/r2
Proponent of evolution
Astronomy, architecture, …
A block of mass m is moving at velocity v0 along a
frictionless, horizontal surface toward a spring with
constant k that is attached to a wall.
a) Find the maximum distance the spring will be
compressed.
b)If the spring is to compress by no more than L m,
what should be the maximum value of v0?
c) How will your answer to (b) change if the spring
force is given by Fx = –kx+nx2 ?
A block of mass M is on a horizontal surface and is attached to
a spring, spring constant k. If the spring is compressed an
amount A and the block released from rest, how far will it go
before stopping if the coefficient of friction between the block
and the surface is ?
How will this answer change is the block is not attached
to the spring??
Consider the spring force given by Fx = –kx+nx2
Consider  = 0 (1 + x/d).

How many joules of energy does 100 watt light
bulb use per hour? How fast would a 70-kg
person have to run to have that amount of
energy?