Transcript Review - Denton ISD

Chapter 6
Work and Energy
Learning Objectives
Work, energy, power

Work and the work-energy theorem

Students should understand the definition of work,
including when it is positive, negative, or zero, so they
can:
• Calculate the work done by a specified constant
force on an object that undergoes a specified
displacement.
• Relate the work done by a force to the area under a
graph of force as a function of position, and calculate
this work in the case where the force is a linear
function of position.
• Use the scalar product operation to calculate the
work performed by a specified constant force F on an
object that undergoes a displacement in a plane.
Learning Objectives
Work, energy, power
 Work and the work-energy theorem
 Students should understand and be able to apply the workenergy theorem, so they can:
• Calculate the change in kinetic energy or speed that
results from performing a specified amount of work on
an object.
• Calculate the work performed by the net force, or by
each of the forces that make up the net force, on an
object that undergoes a specified change in speed or
kinetic energy.
• Apply the theorem to determine the change in an
object’s kinetic energy and speed that results from the
application of specified forces, or to determine the force
that is required in order to bring an object to rest in a
specified distance.
Learning Objectives

Forces and potential energy
 Students should understand the concept of
potential energy, so they can:
• Write an expression for the force exerted
by an ideal spring and for the potential
energy of a stretched or compressed
spring.
• Calculate the potential energy of one or
more objects in a uniform gravitational
field.
Learning Objectives

Conservation of energy
 Students should understand the concepts of mechanical
energy and of total energy, so they can:
• Describe and identify situations in which mechanical energy
is converted to other forms of energy.
• Analyze situations in which an object’s mechanical energy
is changed by friction or by a specified externally applied
force.
 Students should understand conservation of energy, so they
can:
• Identify situations in which mechanical energy is or is not
conserved.
• Apply conservation of energy in analyzing the motion of
systems of connected objects, such as an Atwood’s
machine.
• Apply conservation of energy in analyzing the motion of
objects that move under the influence of springs.
Learning Objectives
Power

Students should understand the definition of power,
so they can:

Calculate the power required to maintain the
motion of an object with constant acceleration
(e.g., to move an object along a level surface, to
raise an object at a constant rate, or to overcome
friction for an object that is moving at a constant
speed).

Calculate the work performed by a force that
supplies constant power, or the average power
supplied by a force that performs a specified
amount of work.
Table of Contents
1.
2.
3.
4.
5.
6.
7.
8.
9.
Work Done by a Constant Force
The Work–Energy Theorem and Kinetic Energy
Gravitational Potential Energy
Conservative Versus Nonconservative Forces
The Conservation of Mechanical Energy
Nonconservative Forces and the Work–Energy
Theorem
Power
Other Forms of Energy and the Conservation of Energy
Work Done by a Variable Force
Chapter 6
Work & Energy
Section 1:
Work Done by a Constant Force
Work



Work tells us how much a force or
combination of forces changes the energy
of a system.
Work is the bridge between force (a vector)
and energy (a scalar).
W = F • d = Fdcos 
 W: work
 F: force (N) (vector)
 d: displacement (m) (vector)
 : angle between force and displacement
Units of Work

SI System: Joule (N m)
 1 Joule of work is done when 1 N acts
on a body moving it a distance of 1
meter
Force and direction of motion
both matter in defining work!


There is no work done by a force if it causes no
displacement.
Forces can do positive, negative, or zero work.
When an box is pushed on a flat floor, for example…
 The normal force and gravity do no work, since
they are perpendicular to the direction of motion.
 The person pushing the box does positive work,
since she is pushing in the direction of motion.
 Friction does negative work, since it points
opposite the direction of motion.
Question 1

If a man holds a 50 kg box at arms length for 2 hours
as he stands still, how much work does he do on the
box?
W=0J
Question 2

If a man holds a 50 kg box at arms length for 2 hours
as he walks 1 km forward, how much work does he
do on the box?
W=0J
Question 3

If a man lifts a 50-kg box 2.0 meters, how much work
does he do on the box?
W = +980 J
Chapter 6
Work & Energy
Section 2:
Work-Energy Theorem & Kinetic
Energy
Work and Energy

Work changes mechanical energy!

If an applied force does positive work on a
system, it tries to increase mechanical energy.

If an applied force does negative work, it tries to
decrease mechanical energy.

The two forms of mechanical energy are called
potential and kinetic energy.
Question 4
Jane uses a vine wrapped around a pulley to lift 70-kg Tarzan to a
tree house 9.0 meters above the ground.
a)How much work does Jane do when she lifts Tarzan?
b)How much work does gravity do when Jane lifts Tarzan?
Question 5
Joe pushes a 10-kg box and slides it across the floor at
constant velocity of 3.0 m/s. The coefficient of kinetic
friction between the box and floor is 0.50.
a) How much work does Joe do if he pushes the box for
15 meters?
b) How much work does friction do as Joe pushes the
box?
Question 6
A father pulls his child in a little red wagon with constant speed. If
the father pulls with a force of 16 N for 10.0 m, and the handle of
the wagon is inclined at an angle of 60o above the horizontal, how
much work does the father do on the wagon?
Kinetic Energy



Energy due to motion
K = ½ m v2
 K: Kinetic Energy
 m: mass in kg
 v: speed in m/s
Unit: Joules
Question 7
A 10.0-g bullet has a speed of 1.2 km/s.
a) What is the kinetic energy of the bullet?
b) What is the bullet’s kinetic energy if the speed is halved?
c) What is the bullet’s kinetic energy if the speed is doubled?
The Work-Energy Theorem


The net work due to all forces equals the change
in the kinetic energy of a system.
Wnet = DK
 Wnet: work due to all forces acting on an object
 DK: change in kinetic energy (Kf – Ki)
Question 8
An 15.0-g acorn falls from a tree and lands on the ground 10.0 m below
with a speed of 11.0 m/s.
a) What would the speed of the acorn have been if there had been
no air resistance?
b) Did air resistance do positive, negative or zero work on the
acorn? Why?
Question 9
An 15.0-g acorn falls from a tree and lands on the ground 10.0 m below
with a speed of 11.0 m/s.
c) How much work was done by air resistance?
d)
What was the average force of air resistance?
Chapter 6
Work & Energy
Section 3:
Gravitational Potential Energy
Potential energy




Energy of position or configuration
“Stored” energy
For gravity: Ug = mgh
 m: mass
 g: acceleration due to gravity
 h: height above the “zero” point
For springs: Us = ½ k x2 (Chapter 10)
 k: spring force constant
 x: displacement from equilibrium position
Chapter 6
Work & Energy
Section 4
Conservative vs non-conservative
forces
Force types




Forces acting on a system can be
divided into two types according to how
they affect potential energy.
Conservative forces can be related to
potential energy changes.
Non-conservative forces cannot be
related to potential energy changes.
So, how exactly do we distinguish
between these two types of forces?
Conservative forces





Work is path independent.
 Work can be calculated from the starting and ending
points only.
 The actual path is ignored in calculations.
Work along a closed path is zero.
 If the starting and ending points are the same, no work is
done by the force.
Work changes potential energy.
Examples:
 Gravity
 Spring force
• Ch 10
Conservation of mechanical energy holds!
Conservative forces and
Potential energy





Wc = -DU
If a conservative force does positive work on a system,
potential energy is lost.
If a conservative force does negative work, potential
energy is gained.
For gravity
 Wg = -DUg = -(mghf – mghi)
For springs
 Ws = -DUs = -(½ k xf2 – ½ k xi2)
More on paths and
conservative forces.Figure from “Physics”,
Q: Assume a conservative force
moves an object along the various
paths. Which two works are equal?
A:
W2 = W3
(path independence)
Q: Which two works, when added
together, give a sum of zero?
A:
W1 + W2 = 0
or
W1 + W3 = 0
(work along a closed path is zero)
James S. Walker,
Prentice-Hall 2002
Question 10
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
A box is moved in the closed
path shown.
a)
How much work is done
by gravity when the box
is moved along the path
ABC?
b)
How much work is done
by gravity when the box
is moved along the path
ABCDA?
Question 11
A diver drops to the water from a height of 40.0 m, his
gravitational potential energy decreases by 25,000
J. How much does the diver weigh?
Chapter 6
Work & Energy
Section 5:
The Conservation of
Mechanical Energy
Law of Conservation of
Energy



In any isolated system, the total energy
remains constant.
Energy can neither be created nor
destroyed, but can only be transformed
from one type of energy to another.
Not true for nuclear reactions (Unit 11)
Law of Conservation of
Mechanical Energy


E = K + U = Constant
 K: Kinetic Energy (1/2 mv2)
 U: Potential Energy (gravity or spring)
DE = DU + DK = 0
 DK: Change in kinetic energy
 DU: Change in gravitational or spring
potential energy
Question 12
Problem copyright “Physics”, James S. Walker, Prentice-Hall 2002
A 0.21 kg apple falls from a tree to the ground, 4.0 m below. Ignoring
air resistance, determine the apple’s gravitational potential energy, U,
kinetic energy, K, and total mechanical energy,
E, when its height above the ground is each of the following: 4.0 m, 2.0
m, and 0.0 m. Take ground level to be the point of zero potential
energy.
Chapter 6
Work & Energy
Section 6:
Nonconservative Forces and the Work–
Energy Theorem
Non-conservative forces





Work is path dependent.
 Knowing the starting and ending points is not
sufficient to calculate the work.
Work along a closed path is NOT zero.
Work changes mechanical energy.
Examples:
 Friction
 Drag (air resistance)
Conservation of mechanical energy does
not hold!
Work done by nonconservative forces


Wnet = Wc + Wnc
 Net work is done by conservative and non-conservative
forces
 Wc = -DU
• Potential energy is related to conservative forces only!
 Wnet = DK
• Kinetic energy is related to net force (work-energy
theorem)
 DK = -DU + Wnc
• From substitution
Wnc = DU + DK = DE
 Nonconservative forces change mechanical energy. If
nonconservative work is negative, as it often is, the
mechanical energy of the system will drop.
Question 13
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
A box is moved in the closed
path shown.
a)
How much work would be
done by friction if the box
were moved along the
path ABC?
b)
How much work is done
by friction when the box is
moved along the path
ABCDA?
Chapter 6
Work & Energy
Section 7
Power
Power





Power is the rate of which work is done.
P = W/Dt
P = F(v)
 W: work in Joules
 Dt: elapsed time in seconds
When we run upstairs, t is small so P is
big.
When we walk upstairs, t is large so P is
small.
Unit of Power


SI unit for Power is the Watt.
 1 Watt = 1 Joule/s
 Named after the Scottish engineer
James Watt (1776-1819) who
perfected the steam engine.
British system
 horsepower
 1 hp = 746 W
How We Buy Energy…





The kilowatt-hour is a commonly used
unit by the electrical power company.
Power companies charge you by the
kilowatt-hour (kWh), but this not power, it
is really energy consumed.
1 kW = 1000 W
1 h = 3600 s
1 kWh = 1000J/s • 3600s = 3.6 x 106J
Question 14
A man runs up the 1600 steps of the Empire State Building in 20 minutes
seconds. If the height gain of each step was 0.20 m, and the man’s mass
was 80.0 kg, what was his average power output during the climb?
Question 15
Calculate the power output of a 0.10 g fly as it walks straight
up a window pane at 2.0 cm/s.
Chapter 6
Work & Energy
Section 8:
Other Forms of Energy and the Law of
Conservation of Energy
Law of Conservation of
Energy



E = U + K + Eint - Wnc= Constant
 Eint is thermal energy.
DU + DK + D Eint - Wnc = 0
Mechanical energy may be converted to
and from heat.
Question 16
Problem copyright “Physics”, James S. Walker, Prentice-Hall 2002
Catching a wave, a 72-kg surfer starts
with a speed of 1.3 m/s, drops through
a height of 1.75 m, and ends with a
speed of 8.2 m/s. How much nonconservative work was done on the
surfer?
Question 17
Problem copyright “Physics”, James S. Walker, Prentice-Hall 2002
A 1.75-kg rock is released from rest at the surface of a pond
1.00 m deep. As the rock falls, a constant upward force of
4.10 N is exerted on it by water resistance. Calculate the
nonconservative work, Wnc, done by the water resistance on
the rock, the gravitational potential energy of the system, U,
the kinetic energy of the rock, K, and the total mechanical
energy of the system, E, for the following depths below the
water’s surface: d = 0.00 m, d = 0.500 m, d = 1.00 m. Let
potential energy be zero at the bottom of the pond.
Chapter 6
Work & Energy
Section 9:
Work done by variable forces
Constant force and work



The force shown is a
constant force.
W = F•Dr can be used to
calculate the work done
by this force when it
moves an object from xa
to xb.
The area under the curve
from xa to xb can also be
used to calculate the
work done by the force
when it moves an object
from xa to xb
F(x)
xa
xb
x
Variable force and work



The force shown is a
variable force.
W = F•Dr CANNOT be
used to calculate the
work done by this force!
The area under the curve
from xa to xb can STILL
be used to calculate the
work done by the force
when it moves an object
from xa to xb
F(x)
xa
xb
x
Problem (Question 18)
Figure from “Physics”, James S. Walker, Prentice-Hall 2002

How much work is done by the force shown when it acts on an object
and pushes it from x = 0.25 m to x = 0.75 m?
Sample Problem (Question 19)
Figure from “Physics”, James S. Walker, Prentice-Hall 2002

How much work is done by the force shown when it acts on an
object and pushes it from x = 2.0 m to x = 4.0 m?