Transcript Work has a specific definition in physics. Work is done anytime a

Work has a specific
definition in physics.
Work is done
anytime a force is
applied through a
distance.
W = F·d
The unit is the
newton•meter,
or joule.
A component of the
force must be in the
direction of the
displacement.
Only this component is
used when calculating
the work.
Example: How much
work is done on a vacuum
cleaner pulled 3.0 m by
a force of 50.0 N at an
angle of 30.0° above
the horizontal?
Work can be positive or
negative depending on
whether the force is in
the same direction as
displacement or in the
opposite direction.
For example: If
you push a box, the
work is positive; but
the work the friction
does is negative.
Kinetic energy
is the energy of
motion.
2
KE = 1/2 mv
KE is a scalar
and the unit is
the joule.
Example: A 7.00 kg bowling ball
moves at 3.00 m/s. How much
kinetic energy does the bowling
ball have? How fast must a
2.45 g table tennis ball move in
order to have the same kinetic
energy as the bowling ball? Is
this reasonable?
The net work done
by a net force acting
on an object is equal
to the change in the
kinetic energy of the
object.
This is called the
work-kinetic energy
theorem:
W = ΔKE
Example: 25 joules of
work is done to a 2 kg
ball. If the ball is not
moving initially, how
fast is it moving after
the work is done?
Example: A person kicks a
10.0 kg sled, giving it an
initial speed of 2.2 m/s.
How far does the sled
move if the coefficient of
kinetic friction between the
sled and the ice is 0.10?
Potential Energy
is stored energy,
energy of possible
motion, energy of
position.
One type of
potential energy
is gravitational
potential energy.
PE = mgh
Example: A 5 kg bunch
of bananas is at the top
of a 6 meter palm tree.
What is the gravitational
potential energy of the
bunch of bananas?
PE = mgh is
just W = Fd.
The unit of potential
energy is the joule.
(The unit of all types of
energy and work is the
joule.)
It is always measured
relative to a zero level.
Another type of potential
energy is Elastic
Potential Energy.
This energy is stored
in a compressed or
stretched object.
The formula for elastic potential
energy is:
PEelastic = 1/2
2
kx
The symbol k is the spring
constant, x is the distance
compressed or stretched.
The spring constant is
a measure of the force
needed to stretch or
compress a spring. It is
measured in newtons
per meter, N/m.
Example: How much
energy is stored in a
spring with a spring
constant of 10 N/m if
it is stretched 2
meters?
Example: A 70.0 kg stuntman is
attached to a bungee cord with
an unstretched length of 15.0 m.
He jumps from a height of 50.0
m. When he stops, the cord has
stretched to 44. 0 m. If k for the
cord is 71.8 N/m, what is the
total PE relative to the ground
when the man stops falling?
When we say
something is
conserved, we
mean it remains
constant.
Mass is a
conserved
quantity.
The motion of many
objects involves a
combination of
potential and kinetic
energy.
The two types of
potential energy
(gravitational and
elastic) plus kinetic
energy form a quantity
called mechanical
energy.
ME = KE + ΣPE
The other types of
energy form
nonmechanical energy.
Mechanical energy
is often conserved.
MEi = MEf
An example
of this is a
pendulum.
Example: A diver
steps off the edge of a
platform that is 10-m
above the water. What
is his velocity when he
hits the water?
Example: If the diver
weighs 500 Newtons,
what is his kinetic
energy when he hits
the water?
Example: What
is the potential
energy of the 500 N
diver while on
the 10 m platform?
Example: Compare
the two answers.
Can you make
some sense of the
results?
MEi = MEf
This is only true if
there is no friction.
MEi = MEf
1/2
2
mv
+
mgh
i
i
=
2
1/2 mv f + mghf
Example: Starting from rest, a
child slides down a frictionless
slide from an initial height of
3.00 m. What is her speed at
the bottom of the slide? Her
mass is 25.0 kg.
How should we do this problem?
If the slope if this
slide were constant,
we could use the
kinematic equations
to solve this problem.
But, we don't
know the slope,
or if it is constant
(acceleration may
not be constant).
But, comparing
energy is not affected
by the shape of the
path, so we don't
need the slope.
We just remember that
MEi = MEf.
Example: Starting from
rest, a child slides down a
frictionless slide from an
initial height of 3.00 m.
What is her speed at the
bottom of the slide? Her
mass is 25.0 kg.
Mechanical energy is
not conserved in the
presence of friction.
(Total energy is
conserved, but not
mechanical.)
Power is the rate
at which work is
done.
P = W/Δt
Since W = Fd
and P = Fd/t
and d/t = v,
P = Fv is also true.
The SI unit of
power is the watt,
which is equal to
one joule per
second.
Machines with
different power
ratings do the same
work in different
time intervals.
Example: Superman
is "more powerful
than a speeding
locomotive." What
does this mean?
Example: A 193 kg curtain
needs to be raised 7.5 m, at
a constant speed, in a time
as close to 5.0 s as possible.
The power ratings for three
motors are 1.0 kW, 3.5 kW,
and 5.5 kW. Which motor is
best?