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Chapter 7. Kinetic Energy and Work
7.1. What is Physics?
7.2. What Is Energy?
7.3. Kinetic Energy
7.4. Work
7.5. Work and Kinetic Energy
7.6. Work Done by the Gravitational Force
7.7. Work Done by a Spring Force
7.8. Work Done by a General Variable
Force
7.9. Power
What is Physics?
Kinetic Energy
Kinetic energy K is energy associated
with the state of motion of an object.
For an object of mass m whose speed v is well
below the speed of light, Kinetic energy K is:
Unit for Kinetic energy is:
Kinetic energy is a scalar quantity.
Work
Work W is energy transferred to or from an
object by means of a force acting on the object.
• Energy transferred to the object is positive work,
• Energy transferred from the object is negative
work.
Finding an Expression for Work
Properties of Work
• Only the force component along the object’s
displacement will contribute to work.
• The force component perpendicular to the
displacement does zero work.
• A force does positive work when it has a vector
component in the same direction displacement,
• A force does negative work when it has a vector
component in the opposite direction.
• Work is a scalar quantity.
Conceptual Example
The figure shows four situations in which a force
acts on a box while the box slides rightward a
distance across a frictionless floor. The
magnitudes of the forces are identical; their
orientations are as shown. Rank the situations
according to the work done on the box by the
force during the displacement, from most positive
to most negative.
Question
A shopping bag is hanging straight down
from your hand as you walk across a
horizontal floor at a constant velocity.
(a) Does the force that your hand exerts on
the bag’s handle do any work? Explain.
(b) Does this force do any work while you
are riding up an escalator at a constant
velocity? Give a reason for your answer.
Example
During a storm, a crate of crepe is sliding across
a slick, oily parking lot through a displacement
while a steady wind pushes against
the crate with a force
. The
situation and coordinate axes are shown in Fig.
7-5. How much work does this
. force do on the
crate during the displacement?
Work Done by Variable Forces
x2
W   Fx ( x)dx
x1
Work Done by a Three-Dimensional Variable Force
The infinitesimal amount of work dW done on
the particle by the force is dW  F (r )  dr
The work W done by while the particle moves from an initial
position with coordinates (x1, y1, z1) to a final position with
r2
coordinates (x2, y2, z2) is then
W   F (r ) dr
r1
Net Work–Kinetic Energy Theorem
When a net external force does work Wnet
on an object, the change of kinetic energy
of the object equals to the net work:
W net  KE f  KEi
W
net
r2
  F net (r ) dr
r1
Units of work and energy are: 1 joule = 1 J =1 kg∙m2/s2 = 1 N∙m
Conceptual Example Work and Kinetic Energy
Figure illustrates a satellite
moving about the earth in
a circular orbit and in an
elliptical orbit. The only
external force that acts on
the satellite is the
gravitational force. For
these two orbits,
determine whether the
kinetic energy of the
satellite changes during
the motion.
EXAMPLE
A 2.0 kg stone moves along an x axis on a horizontal
frictionless surface, acted on by only a force Fx(x) that
varies with the stone's position as shown in Fig.
• (a) How much work is done on the stone by the force as
the stone moves from its initial point at x1 = 0 to x2 = 5 m?
• (b) The stone starts from rest at x1 = 0 m. What is its
speed at x = 8 m?
Checkpoint 1
A particle moves along an x axis. Does the
kinetic energy of the particle increase,
decrease, or remain the same if the
particle’s velocity changes
(a) from −3 m/s to −2 m/s and
(b) from −2 m/s to 2 m/s?
(c) In each situation, is the work done on the
particle positive, negative, or zero?
EXAMPLE
During a storm, a crate of crepe is sliding across a slick,
oily parking lot through a displacement
while a
steady wind pushes against the crate with a force
The situation and coordinate axes are shown in Fig.
(a)How much work does this force from the wind do on the crate during
the displacement?
(b)If the crate has a kinetic energy of 10 J at the beginning of
displacement , what is its kinetic energy at the end of assuming F  F ?
net
Example: Deep Space
• The space probe Deep Space 1 was launched October
24, 1998. Its mass was 474 kg. The goal of the mission
was to test a new kind of engine called an ion propulsion
drive, which generates only a weak thrust, but can do so
for long periods of time using only small amounts of fuel.
The mission has been spectacularly successful. Consider
the probe traveling at an initial speed of v0=275 m/s. No
forces act on it except the 56.0-mN thrust of its engine.
This external force F is directed parallel to the
displacement s of magnitude
. Determine the
final speed of the probe, assuming that the mass remains
nearly constant.
Example
Three Forces Figure shows three forces applied
to a trunk that moves leftward by 3.00 m over a
frictionless floor. The force magnitudes are
FA = 5.00 N, FB = 9.00 N, and FC = 3.00 N. During
the displacement, (a) what is the net work done
on the trunk by the three forces and (b) does the
kinetic energy of the trunk increase or decrease?
Example
The skateboarder in Figure a is coasting down a ramp,
and there are three forces acting on her: her weight W
(magnitude=675 N), a frictional force f (magnitude=125
N) that opposes her motion, and a normal force FN
(magnitude=612 N). (a) Determine the net work done by
the three forces when she coasts for a distance of 9.2
m. (b) If the skateboard’s initial speed is zero, what will
be her final kinetic energy?
Work Done by the Gravitational Force
Work done on the ball by the gravity is:
Wgravity  Fy (h f  hi )  mg (h f  hi )  (mgh f  mghi )
If an object is moving down, W
gravity  0
•If an object is moving up,
Wgravity  0
Work done by the gravity only depends
on the change of height, not depends on
the path.
Work Done by a Spring Force
The spring force given by
Hooke’s Law:
spring
x
F
 k x
The work done by spring
force:
1
1
W spring  ( kx22  kx12 )
2
2
Example
•
In Fig., a horizontal force Fa of magnitude 20.0 N is applied to a
3.00 kg psychology book as the book slides a distance d=0.500m
up a frictionless ramp at angle θ=30 degrees. (a) During the
displacement, what is the net work done on the book by Fa , the
gravitational force on the book, and the normal force on the book?
(b) If the book has zero kinetic energy at the start of the
displacement, what is its speed at the end of the displacement?
Example
The only force acting on a 2.0 kg body as it
moves along a positive x axis has an x
component , with x in meters. The velocity
at is 8.0 m/s. (a) What is the velocity of
the body at ? (b) At what positive value of
x will the body have a velocity of 5.0 m/s?
Power
The rate at which work is done by a force
is called the power.
• The average power due to the work done by a force
during that time interval as
• We define the instantaneous power P as the
instantaneous rate of doing work, so that
The units of power
Sample Problem
• Figure 7-16 shows constant forces F1 and F2 acting on
a box as the box slides rightward across a frictionless
floor. Force F1 is horizontal, with magnitude 2.0 N; force
F2 is angled upward by 60° to the floor and has
magnitude 4.0 N. The speed v of the box at a certain
instant is 3.0 m/s. What is the power due to each force
acting on the box at that instant, and what is the net
power? Is the net power changing at that instant?