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Energy Review
Brandon Demory
Ch 7 and Ch 8 (p408-433)
Ch14(all)
Overview
Energy- the ability to do work
Types of energy:
1. Kinetic: The energy associated with
motion. K=½mv2
2. Potential: The energy associated with
position. Two particular types are
gravitational potential energy and elastic
potential energy. U= mg (yf - yi) and U=
½kx2. ∆U= -∫ F(x)dx.
Work
Work: energy transferred to or from an object via a
force acting on the object. It is also the integral of a
variable force.
W= Fd or Fd cos(θ) or F→ dot d→.
Work- Kinetic Energy Theorem
The change in Kinetic Energy of an object is equal to the
net work of an object. ∆K= W= Kf –Ki= Wapplied + Wgrav
Work done by a gravitational force is defined as: W= mgd cos(θ).
F=ma;
v2= vo2 +2ad;
½mv2 - ½mvo2= Fd
The net work on an object is equal to the sum of the works done by the
forces.
Work cont.
Work done by a spring force: W= ½kxi2 - ½kxf2.
For a variable force, we take the integral of the force over
the distance interval. W= ∫F∆x or ∫F dx
For work in more than one dimension, the sum of the work
components equals the total work.
W= ∫Fx dx + ∫Fy dy + ∫Fz dz.
Power
- The time rate at which work is done by a force.
Pavg= W/∆t; Pavg= ∆E/∆t
-Instantaneous power is the instantaneous time rate of doing
work. P= dW/dt.
Power is also the Force dot the velocity. (instantaneous
power)
P= Fd; P= dW/dt= F cos(θ) dx/dt= Fv cos(θ)
P= dE/dt
Mechanical Energy
-The sum of the Potential and Kinetic Energy of a system.
Emec = K + U
-For an isolated system, the mechanical energy of the
system is conserved. U1 + K1 = U2 + K2.
-From this we can see that: ∆Emec= 0 = ∆K + ∆U
W= ∆Emec. This is work done on a system by an external
force.
(friction involved) W= ∆Emec + ∆Eth; ∆Eth= f*d (frictional
force; sliding)
Conservation of Energy
- The total energy of a system can change only by
amounts of energy that are transferred to or from the
system.
- In an isolated system, the total energy cannot change.
Therefore: ∆Emec + ∆Eint= 0
Conservative force
• The work done by a conservative force on a
particle moving between two points does not
depend on the path taken by the particle.
• So, for a round trip, the net work done by the
conservative force is zero.
Wab,1 + Wba,2 = 0; Wab,1 = -Wba,2
For path ab2, the work done by the force to go from a to b is the opposite
of the work to go from b to a. therefore, Wab2 = -Wba,2
Using substitution of Wab2 for –Wba,2, we find:
Wab,1 = Wab2
How do you find the work done by
a variable force?
You must take the integral of
the force. W= ∫F∆x
In an isolated system, the change
in energy always adds up to
_____.
zero
The kinetic energy of a system is
always _______ or zero and
never ______.
Positive, negative
The Work- Kinetic Energy theorem
states that:
∆K= Wnet= Kf –Ki
The sum of the Kinetic energy and
potential energy of a system is
the ________.
The Mechanical energy
Power is _____.
The time rate at which work is
done
For an object falling at a constant velocity, which
of the following does not change for the
system.
A) Total energy
B) kinetic energy
C) Wavelength D) potential energy
B) Kinetic energy
The formula for spring potential
energy is:
U=½kx2
The net work done on an object
is______:
The sum of the individual works
An object of mass 1 kg moving at
2 m/s has a kinetic energy of
____.
2 Joules
The units for all forms of energy
are ____.
Joules
The formula for work is:
Fd cos()
All of the following are ways to describe
power except:
a) W/∆t
b) dE/dt
c) Fv cos(θ)
d) Fd cos(θ)
D) Is correct
Two ways to describe a
conservative force_____.
One in which the net work the
force does on the particle
moving around any closed path
from a starting point back to
that point is zero. Or a path
independent force.
Gravitational Potential Energy is
defined as:
U= mgh
Energy is conserved in a system
if:
There is no external force
acting on the system.
A 2.0 kg mass hanging 3 meters
from the ground has a
gravitational potential energy
of; g= 10 m/s2
U= 60 Joules
Friction is a conservative or nonconservative force?
Non-conservative force
What is the velocity of a 3 kg
object that has a kinetic energy
of 24 Joules?
4 m/s
True of False:
Worknet = -U (potential energy)
True
A mass of 1 kg has a Kinetic
energy of 8 Joules. 28 joules of
work are applied to the mass.
Find its new velocity.
W=Kf-Ki; 28=K-8;
K=36=.5*1*v2.
V=√72 m/s
A mass of 1 kg is attached to an oscillating
spring with a spring constant of 4N/m. At
equilibrium, the spring has 18J of Kinetic
energy. Find the maximum amplitude of
its oscillation if there are no external
forces in the system.
X= 3 meters
A helicopter lifts a 36 kg mass 4
meters vertically from the ocean.
How much work is done by the
gravitational force?
-1.4Kj
Power is measured in______.
Watts
An object with an instantaneous
velocity of 3 m/s that has a
constant force of 2N applied to
itself has an instantaneous
power of:
6 Watts
An object (mass 2 kg) has an initial velocity of 3 m/s. The
frictional force on the object is a constant 1N.
a) How far will the object slide before it stops?
b) If it took 3 seconds for the box to stop moving, what
was the average power?
a) D=9 meters
b) Pavg=3 watts
If a person lifts on object to a
higher height, is the work done
by gravity positive or negative
work?
Negative Work
True or False
Instantaneous Power is defined as
P= ∆E/∆t
False; it is actually dE/dt
For an isolated system,
if an object starts with 20 Joules of K energy
and 10 Joules of U, and at another
instant, has 16 joules of U, what is the
Kenergy of the object?
14 Joules
For a force defined by the
function F=3x; the work done in
the system as the object moves
from x=1 to x=3 is?
W=∫Fdx= ∫3x dx=(3/2)x2;
W=(3/2)(32-12)=12 joules