Transcript Work and Energy

Work and Energy
No vectors!
Work
• Work has a specific meaning in physics
• Work is a force applied over a distance.
• Understand that work is done ON something
and that something then moves
• Equation for work is Work = Force X Distance
• W = FD
Example – A powerlifter
• A force is exerted on a
bar and that bar and
• That bar is MOVED by
the force
• The bar then moves
THROUGH A DISTANCE
• How much work is he
doing standing there
holding the bar still?
http://powerliftinghub.com/images/andy.jpg
Work concepts
• Work doesn’t care about direction (it’s not a
vector)
• Let’s say you apply 5 N to an object to move it
2 meters. What is the work done?
• Now say you double the distance. How does
the work done change?
5N
2m
Work concepts questions
• Now say you double the distance you apply a
force. How does the work done change?
• Let’s say that instead, you keep the same
distance, but apply twice as much force. How
does the work done change?
• Let’s say you now go crazy psycho and apply
twice the force over twice the distance. How
does the work done change?
For those who were paying attention
during the momentum chapter…
• What is the difference between work and
impulse?
• Work is force applied over a distance
• Impulse is a force applied during a period of
time
Work’s Units
• The units for work are called Joules (rhymes
with ‘cools’).
• If work = force X distance, and force is in
Newtons and distance is in meters, then…
• 1 Joule = 1 Newton•meter
Power
• Power is work done in a certain time interval
• The units of power are
– Watts (you probably have heard of this from the
ratings on light bulbs) or
– Kilowatts (as you may know from the electric
meter on your house)
– Horsepower (as you may know from your car
engine)
Relating the esoteric to the everyday…
• Lifting a quarter pounder with cheese 1 meter
in 1 second is roughly one Watt.
• Lifting a 225 pound man 1 meter in one
second is roughly one kilowatt.
And now, it’s time to run up and down
the stairs
• Work done against gravity = weight X height
change
• Remember, weight is a force and height is a
distance, so work done = mgh, where
m=mass, g = 9.8m/s2 and h = height
• Your power output is your work done against
gravity divided by your time.
• Let’s go!
Mechanical Energy
• Mechanical energy is the total amount of
energy in a system.
• Mechanical energy is the sum of 2 kinds of
energy:
– Potential energy
– Kinetic energy
• In the absence of friction and air resistance,
mechanical energy is conserved
Potential Energy
• An object may store energy simply because of
its position.
• This stored energy is called potential energy,
because it has the potential to do work.
– Examples: a compressed spring, a stretched
rubber band, etc.
• If an object is raised to a height h above the
floor, then it has gravitational potential
energy.
Gravitational Potential Energy
• Gravitational PE = weight X height
• Weight = mg, height = h
• So PE = mgh
– m = mass in kg, h = height in meters, g=9.8m/s2
• For gravitational PE, all you care about is the
height above the ground or floor. It doesn’t
matter how it got there or what path it takes
when it falls.
PE Questions
• How much work is done on a 100N boulder
that you carry horizontally across a 10m
room? What is the boulder’s change in PE?
• How much work is done on a 100N boulder
that you lift vertically 1m?
• What power is expended if you lift that
boulder 1m in 1 sec?
• What is the boulder’s gravitational PE in the
lifted position?
Kinetic Energy
• Kinetic Energy is the energy of something in
motion
• KE = ½ mv2
• Work and energy are related (and have the
same units)
• Work done on an object = change in KE
– So: Fd = ½ mv2
• Note that velocity is squared. How does the KE
of an object change if you double the speed?
Stopping distances
• Friction is the force that causes a car to slow
to a stop when you slam on the brakes.
• Friction applied over a distance = work, and
that work will decrease the KE of the car
• Typical stopping distances:
– Speed = 30 km/hr, skid = 10m
– Speed = 60 km/hr, skid = 40m
– Speed = 120 km/hr, skid = 160m
Conservation of Energy
• The Law of Conservation of Energy says:
– “energy cannot be created or destroyed. It can be
transformed from one form to another, but the
total amount of energy never changes.”
• That means that the total energy of a system
stays the same
• E = PE + KE, and this remains constant
Conservation of Energy
http://www.physicsclassroom.com/class/energy/u5l2b21.gif
Conservation of Energy
http://serc.carleton.edu/images/sp/library/uncertainty/diagram_conservation_energy_si.jpg
Energy of a Pendulum
• At position A, the
pendulum has only PE
• Between A and B, it has a
mix of PE and KE (with PE
decreasing and KE
increasing)
• At B, it has purely KE
• Between B and C, it has a
mix again (with KE
decreasing and PE
decreasing)
Machines
• A machine is something that multiplies force
or changes the direction of a force.
• In general an important concept with
machines is that work input = work output
• Remember that work = force X distance
• So, (force X distance)input =
(forceXdistance)output
Levers
http://www.sciencelearn.org.nz/var/sciencelearn/storage/images/contexts/sporting_edge/sci_media/
mechanical_advantage/17442-5-eng-NZ/mechanical_advantage_full_size_landscape.jpg
Levers Continued
How does this work?
• The girl’s input force is
labeled “effort”
• The input distance = the
length of the lever arm
to the pivot point
• The load moved is very
heavy
• The distance on the
load side of the pivot is
very short
Lever in action
Levers continued
• So the input work of the girl is her force X the
lever arm distance
• The output work is the load weight X the short
distance of the lever
• Let’s say the load was 200 N. Then let’s say that
the lever arm is 10 m and the short side of the
lever is 1m. What does the girl’s input force need
to be to lift the boulder?
• (F)(10m) = (200N)(1m), so F = (200N)(1m)/(10m)
• F = 20 N
Levers yet again
• So, the advantage of the lever system is that
you put in less force to move a heavy object.
• The disadvantage is that the object doesn’t
move very far.
• But hey, what do you want?
Mechanical advantage
• The ratio of the output force to the input force
is called the Mechanical advantage.
• In the previous lever problem, the ratio was
200N/20 N = 10x
• Let’s do some mechanical advantage
demonstrations.
Incline planes and pulleys
• An incline plane is a way to get a heavy load
moved vertically upwards.
• The mechanical advantage of an incline plane is
the ratio of length of incline to the vertical
distance raised.
– Example: a 6 m incline that has one end raised up 1m
has a mechanical advantage of 6x. You only have to
apply 1/6 of the weight of the load to push it up the
ramp.
• Systems of pulleys can also be used for
mechanical advantage.