Transcript 7-4 Kinetic Energy and the Work-Energy Principle This means that

Chapter 8
Conservation of Energy
7.4 kinetic Energy and workenergy principle
8.1 Conservative forces
8.2 Potential Energy
8.3 Mechanical Energy and
Its Conservationial Energy
8.4 Problem Solving Using
Conservation of Mechanical
Energy
Question
If you have a variable Force, you can find the
work by finding:
A) The area under a curve of Force as a
function of time
B) The area under a curve of Force as a
function of displacement
C) The slope curve of Force as a function of
time
D) The slope of a curve of Force as a
function of displacement
7-4 Kinetic Energy and the Work-Energy
Principle
Example 7-8: Work on a car, to increase its
kinetic energy.
How much net work is required to accelerate
a 1000-kg car from 20 m/s to 30 m/s?
The net work is the increase in kinetic
energy
7-4 Kinetic Energy and the Work-Energy
Principle
Example 7-10: A compressed spring.
A horizontal spring has spring constant k = 360 N/m. (a) How
much work is required to compress it from its uncompressed
length (x = 0) to x = 11.0 cm? (b) If a 1.85-kg block is
placed against the spring and the spring is released, what will
be the speed of the block when it separates from the spring at
x = 0? Ignore friction. (c) Repeat part (b) but assume that the
block is moving on a table and that some kind of constant drag
force FD = 7.0 N is acting to slow it down, such as friction (or
perhaps your finger).
Problem 56
56. (II) An 85-g arrow is fired from a
bow whose string exerts an average force
of 105 N on the arrow over a distance of
75 cm. What is the speed of the arrow as
it leaves the bow?
7-4 Kinetic Energy and the Work-Energy
Principle
Energy was traditionally defined as the ability
to do work. All forces are able to do work;
however, we are dealing in these chapters with
mechanical energy, which does follow this
definition.
7-4 Kinetic Energy and the Work-Energy
Principle
If we write the acceleration in terms of
the velocity and the distance, we find that
the work done here is
We define the kinetic energy as:
7-4 Kinetic Energy and the Work-Energy
Principle
This means that the work done is equal to the
change in the kinetic energy:
•This is the Work-Energy Principle
• If the net work is positive, the kinetic
energy increases.
• If the net work is negative, the kinetic
energy decreases.
7-4 Kinetic Energy and the Work-Energy
Principle
Because work and kinetic energy can be
equated, they must have the same units:
kinetic energy is measured in joules. Energy
can be considered as the ability to do work:
8-1 Conservative and
Nonconservative Forces
2
1
Example 8-1: How
much work is needed
to move a particle
from position 1 to 2?
8-1 Conservative and Nonconservative
Forces
A force is conservative if:
the work done by the force on an object
moving from one point to another depends only
on the initial and final positions of the
object, and is independent of the particular
path taken.
Example: gravity.
W=-mg (y2-y1)
8-1 Conservative and Nonconservative
Forces
Another definition of a conservative force:
a force is conservative if the net work done by
the force on an object moving around any
closed path is zero.
(a)
(b)
8-1 Conservative and Nonconservative
Forces
If friction is present, the work done depends
not only on the starting and ending points, but
also on the path taken. Friction is called a
non-conservative force.
W = FPd
8-1 Conservative and Nonconservative
Forces
8-2 Potential Energy
Example 8-2
What potential energy is
needed to move a block
upward with an external
force Fext?
8-2 Potential Energy
In raising a mass m to a
height h, the work done by
the external force is
.
We therefore define the
gravitational potential
energy at a height y above
some reference point:
.
8-2 Potential Energy
Example 8-3: Potential energy changes for a roller
coaster.
A 1000-kg roller-coaster car moves from point 1 to
point 2 and then to point 3. (a) What is the
gravitational potential energy at points 2 and 3
relative to point 1? That is, take y = 0 at point 1.
(b) What is the change in potential energy when the
car goes from point 2 to point 3? (c) Repeat parts
(a) and (b), but take the reference point (y = 0) to
be at point 3.
Problem 7