Work and Power
Work
• Let’s look at some examples of moving a book
where “work” is being done and “work” is not
being done on the book.
• Move the book from the table to a higher
height.
• Move the book from the higher height back
the table.
• Sliding the book on the table
• Lifting the book and putting it back down
Work
• Physics definition – work is done on an object
when the object’s energy is changed.
• Lifting the book – raising the gravitational
potential energy
• Sliding the book – raising the kinetic energy
• As the book slides and stops, lowering the
kinetic energy
Mathematical definitions of Work
• Work is scalar (magnitude only)
• Work = Force*Displacement
– This causes a change in energy usually, especially
when lifted a displacement
– Only the force parallel to the motion
• Ex: Gravity does not do work on a box being slid across
a table.
• Work = change in kinetic energy
• Work = change in potential energy
English vs. Physics
• Suppose you hold a textbook over your head:
Is work being done?
• Though the English definition might suggest
that you are doing work since you will get
tired after a while, the physics definition says
that no work is done on the book because
there is no change in energy of the book
• Work is being done on my arm since I am
using the chemical potential energy in the
muscles.
Two categories of work
1) Work done to raise the energy of an object
– This is called positive work
– Ex: Raising an object off of a table is raising the
gravitational potential energy of the book
2) Work done to lower the energy of an object
– This is called negative work
– Ex: A box sliding on a table stops due to friction.
The friction is doing negative work on the box
because it is taking away kinetic energy.
Units for Work
• Joule (rhymes with “cool”) is the unit for
work… it is also the unit for energy (more
about this tomorrow)
• 1 Joule would be like lifting an apple from the
ground to a table top. (1 Newton weight up
one meter).
• Stopping a truck going 60mph is takes about 1
million Joules of work.
Other Units for Energy (and Work)
• calorie and Calorie
Power
• Which takes more power:
– Slowly raising a book to the table top?
– Quickly raising the book to the table top?
• The definition of work says nothing about
“how long” the change in motion will occur in
time.
• It takes the same amount of work to lift a box
up the stairs if you run up the stairs in 4
seconds, or if you walk up the stairs in 30
seconds.
Power
• Power is the rate at which work is done.
• Something that is more powerful will do more
work in the same amount of time as
something that is not as powerful.
• Ex: An old microwave can heat up a hot
pocket in about 3 minutes. A new microwave
can heat up the hot pocket to the same
temperature in about 2 and a half minutes.
• The new microwave is more powerful.
Power
• A car with more power can change its speed
from a stop up to 60 mph in a faster amount
of time than the same change in speed for a
less powerful car of the same weight.
Units for Power
• Metric Units – Watt
– One Watt of power is lifting an apple onto a table
within one second.
• English Units – Horsepower
– 1 horsepower is the same as 750 Watts
Power definition in mathematics
• Power is the rate of change of work:
• Power = work done/time
Gravitational potential energy
• Depends on the mass of the object and how
high the object is away from a reference
point (usually the ground or a table top)
• Mathematically:
• GPE = mgh, where g is 10 m/s2
Kinetic Energy
• The energy of motion.
• Depends on the mass of the object as well as
the speed of the object
• Mathematically:
• KE = ½ mv2
Conceptual ? On KE
• A 4 kg bicycle changing its speed from 5 m/s
to 10 m/s.
• A 4 kg bicycle changing its speed from 10 m/s
to 15 m/s.
• Which requires more work and why?