Download File

Chapter 5
Work and Energy
Part 1
Work
Section 1 Objectives
• Recognize the difference between the
scientific and the ordinary definitions of
work.
• Define work by relating it to force and
displacement.
• Identify where work is being performed in
a variety of situations.
• Calculate the net work done when many
forces are applied to an object.
Definition of Work
• Clip 595
• Work is done on an object when a force
causes a displacement of the object.
• Work = Force X Distance
– w = Fd
• Work can only be done in the direction of
the force.
Work con’t
• Is there work being
performed?
• Why or why not
Work con’t
• What happens when you apply a force at
an angle?
• Imagine you are pushing a crate across
the floor.
d
θ
F
Work con’t
• Only the horizontal component of you
applied force causes a displacement.
• Work in our crate problem is
– W = Fdcosθ
• If many forces are acting on an object then
we write the equation as
• Wnet = Fnetdcosθ
SI Units for Work
• Work has the dimensions of force times
length.
• So, work has the units of Newton x meter
or Joules
• Work is positive when displacement is in
the same direction of the force, and
negative when opposite of the force.
Sample Problem A
• How much work is done on a vacuum cleaner
pulled 3.0 m by a force of 50 N at an angle of
30.0° above the horizon?
• A tugboat pulls a ship with a constant net
horizontal force of 5000 N and causes a ship to
move through a harbor. How much work is done
on the ship if it moves a distance of 3.00 km?
• If 2.0 J of work is done in raising an 180 g apple,
how far is it lifted?
Today’s Homework
• P. 162 2,3
• P. 163 1-6
• P. 184 1-10
Section II
Energy
Section II Objectives
• Identify several forms of energy.
• Calculate kinetic energy for an object
• Apply the work-kinetic energy theorem to
solve problems.
• Distinguish between kinetic and potential
energy
• Classify different types of potential energy
• Calculate the potential energy associated
with an objects position.
Kinetic Energy
• Kinetic energy is associated with an object
in motion.
• Kinetic energy depends on speed and
mass.
• KE = ½ mv2
– Kinetic energy = ½ X mass X (speed)2
• Clip 318
Sample Problems B
• A. 7.0kg bowling ball moves at 3.00 m/s.
How fast must a 2.45 g table tennis ball
move in order to have the same kinetic
energy as the bowling ball?
• What is the speed of a .145 kg baseball if
its kinetic energy is 109J?
The Work-Energy Theorem
• Defined as
– The net work done by all the forces acting on
an object is equal to the change in the object’s
kinetic energy.
– Wnet = ∆KE
= ½ mvf2 – ½ mvi2
Sample Problem C
• On a frozen pond, 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 .10.
• A 2000 kg car accelerates from rest under the actions of
two forces. One is a forward force of 1140 N provided by
the traction between the wheels and the road. The other
is a 950 N resistive force due to various frictional forces.
Use the work-kinetic energy theorem to determine how
far the car must travel for its speed to reach 2.0 m/s.
• A 75 kg bobsled is pushed along a horizontal surface by
two athletes. After the bobsled is pushed a distance of
4.5 m starting from rest, its speed is 6.0 m/s. Find the
magnitude of the net force on the bobsled.
Potential Energy
• Potential energy is stored energy. It is energy
associated with an object because of the
position, shape, or condition of the object.
• Gravitational potential energy depends on height
from zero level.
• PEg = mgh
– Gravitational potential energy
= mass X gravity X height
• PEelastic = ½ kx2
– Elastic potential energy
= ½ spring constant X (distance)2
• Clip 320 & 321
Sample Problem D
• A 70.0 kg stuntman is attached to a bungee cord with an
unstretched length of 15.0 m. He jumps off a bridge
spanning a river from a height of 50.0m. When he finally
stops, the cord has a stretched length of 44.0m. Treat
the stuntman as a point mass, and disregard the weight
of the bungee cord. Assuming the spring constant of the
bungee cord is 71.8 N/m, what is the total potential
energy relative to the water when the man stops falling?
• The staples inside a stapler are kept in place by a spring
with a relaxed length of .115 m. If the spring constant is
51.0 N/m, how much elastic potential energy is stored in
the spring when its length is .015 m?
Today’s Homework
•
•
•
•
•
P 166 1, 3, 5
P 168 1, 3
P 172 1, 3
P 172 (Section Review) 1 – 4
P 184 11 – 14, 23 - 25
Section 3
Conservation of Energy
Section Objectives
• Identify situations in which conservation of
mechanical energy is valid.
• Recognize the forms that conserved
energy can take.
• Solve problems using the conservation of
mechanical energy.
Conserved Quantities
• When something is conserved it means
constant.
– It can change, but the amount must be the
same.
• Example
– Conservation of mass - if a light bulb shatters on the
ground. No matter how many pieces the total mass of the
pieces will equal the mass of the light bulb.
Mechanical Energy
• Mechanical Energy is defined as the sum of the
kinetic and all of the forms of potential energy
associated with an object or a group of objects.
• ME = KE + PE
• Mechanical energy is conserved
• MEi = MEf
– KEi + PEi = KEf + Pef
– 1/2mvi2 + mghi = 1/2mvf2 + mghf
• See Clip 567
Mechanical Energy of a Swing
• What is happening to
the energy at each
point?
– 1) KE = 0; ME = PE
1
5
4
2
3
Sample Problem E
• Starting from rest, a child zooms down a
frictionless slide from an initial height of 3.00 m.
What is her speed at the bottom of the slide?
Assume she has the mass of 25.0 kg.
• A 755 N diver drops from a board 10.0 m above
the water’s surface. Find the diver’s speed 5.00
m above the water’s surface. Then find the
diver’s speed just before striking the water.
• An Olympic runner jumps over a hurdle. If the
runner’s initial vertical speed is 2.2 m/s, how
much will the runner’s center of mass be raised
during the jump?
Today’s Work
• P 177 1 - 5
• P 178 1 - 3
• P 186 26, 28, 30, 31, 33, 34
Section 4
Power
Rate of Energy Transfer
• Power
– See Clip 322
– The rate at which work is done
– A quantity that measures the rate of which work is
done or energy is transformed.
– P = W/t
• Power = Work  Time Interval
– P = Fv
• Power = Force X speed
– The Unit for Power is the watt, W.
• ( 1 joule per second)
• Horsepower is also a unit for power , it is equal to 746 watts.
Sample Problem F
• A 193 kg curtain needs to be raised 7.5 m, at a
constant speed, in as close to 5.0 sec. as
possible. The Power ratings for three motors are
listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which
motor is best for the job?
• A car with a mass of 1500 kg starts from rest
and accelerates to a speed of 18.0 m/s in 12.0 s.
Assume the force of resistance remains constant
at 400 N during this time. What is the average
power developed by the car’s engine?
• How long does it take a 19kW steam engine to
do 6.8 x 107 J or work?
Today’s Homework
• P181 Practice F 1, 3, 5
• P181 1, 2, 4
• P 186 35, 36