Chapter 6
Work and Energy
Forms of Energy
• Mechanical
• Kinetic, gravitational
• Thermal
• Microscopic mechanical
• Electromagnetic
• Nuclear
Energy is conserved!
Bowling ball video
Conservation of energy
• https://www.youtube.com/watch?v=mhIOylZMg6
Q
• Conservation of energy
Roller Coaster Conservation of
Energy
• https://www.youtube.com/watch?v=LrRdKmjhOgw
Work examples
• Pushing a heavy suitcase requires a lot of energy or
WORK. The heavier the suitcase and the longer
distance you push it, the more work is done.
Units of Work and Energy
W  Fx
SI unit = Joule
1 J = 1 Nm = 1 kgm2/s2
Example 1: Work
• You push a 20kg box a distance of 2.5 meters. How
much work is done?
• You measured the amount of work you put in after
pulling bag of potatoes to be 50 J. You know that
the potatoes weigh 10 kg and you accelerated 0.8
m/s. What was the distance you traveled.
Work
• Relates force to change in energy
r r
r
W  F  ( x f  xi )
 Fx cos
• Scalar quantity
• Independent of time
Example 2: Work
• A boat is put into the water from a ramp that makes
an angle of 60 degrees. The boat slides a distance of
5.0 meters down the ramp. The boat weighs 4900 kg.
How much work does gravity do on the boat?
How about you are pushing
something and it doesn’t move?
•
•
•
•
Are you doing any work?
Why or why not?
Think of the equation…
Why do you get tired?
Work can be positive or negative
• Work is positive if the force has a component that is
in the direction of motion.
• Work is negative if the force has a component that is
opposite to the direction of motion.
• Work is zero if there is no motion.
Work can be positive or negative
• Man does positive work
lifting box
• Man does negative work
lowering box
• Gravity does positive work
when box lowers
• Gravity does negative work
when box is raised
The work done by separate forces
can be summed
• W total=W1+W2+W3….
• Since the work can be positive or negative, it is
possible for the work to be zero (or below) even
though individual amounts of work are nonzero and
positive.
• Pg. 195 in the textbook
Section 6.2 and 6.3 Work and Energy
• Key terms:
• Kinetic energy
• Potential energy
• Mechanical energy
• Elastic energy
Kinetic energy
• Energy due to motion of an object. When you go
down a hill you are creating more kinetic energy as
the car speeds up.
• Measured in Joules (J)
• Kinetic energy is increased if mass or velocity
increases.
• Think of a child vs. a large adult sliding to first base..
Kinetic Energy
1 2
KE  mv
2
Same units as work
Remember the Eq. of motion
2
vf
vi2

 ax
2
2
Multiply both sides by m,
1 2 1 2
mv f  mvi  max
2
2
KE f  KEi  Fx
Example 3
A skater of mass 60 kg has an initial velocity of 12
m/s. He slides on ice where the frictional force is 36
N. How far will the skater slide before he stops?
Work and kinetic energy are related
• Total work done on an object is equal to the change
in its kinetic energy
• 0.5(m)(vf)2 – 0.5(m)(vi)2 =Work total
Example 4
• How much work is required for a 74 kg sprinter to
accelerate from rest to a speed of 2.2 m/s?
• Vi=0
• Vf=2.2m/s
• M=74kg
Potential Energy
If force depends on distance,
PE  Fx
For gravity (near Earth’s surface)
PE  mgh
Example 5
• Find the potential energy of a 60kg person standing
on a building that is 10meters high?
• A candy bar has a nutritional value of 880,000J. If a
80kg mountain climber eats a bar and converts all the
energy to potential energy (not realistic) how much
altitude can the climber gain?
Potential Energy of Spring
1
 PE  (kx)x
2
PE=-Fx
1 2
PE  kx
2
F
x
Springs (Hooke’s Law)
F  kx
Proportional to
displacement from
equilibrium