Transcript Review 29:008 Exam 2

Review
29:008
Exam 2
Ch. 6 Energy & Oscillations
Kinetic Energy, and the Work-Energy
Principle
Apply a force to accelerate a bus:
the work done here is
We define the kinetic energy:
6-3 Kinetic Energy, and the Work-Energy
Principle
This means that the work done is equal to the
change in the kinetic energy:
(6-4)
• If the net work is positive, the kinetic energy
increases.
• If the net work is negative, the kinetic energy
decreases.
6-3 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.
6-4 Potential Energy
An object can have potential energy by virtue of
its surroundings.
Familiar examples of potential energy:
• A wound-up spring
• A stretched elastic band
• An object at some height above the ground
Potential Energy
In raising a mass m to a height
h, the work done by the
external force is
(6-5a)
We therefore define the
gravitational potential energy:
(6-6)
Potential Energy
This potential energy can become kinetic energy
if the object is dropped.
If
, where do we measure y from?
It turns out not to matter, as long as we are
consistent about where we choose y = 0. Only
changes in potential energy can be measured.
Potential Energy
Potential energy can also be stored in a spring
when it is compressed; the figure below shows
potential energy yielding kinetic energy.
6-4 Potential Energy
The force required to
compress or stretch a
spring is:
where k is called the
spring constant, and
needs to be measured for
each spring.
Potential Energy
The force increases as the spring is stretched or
compressed further. We find that the potential
energy of the compressed or stretched spring,
measured from its equilibrium position, can be
written:
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
nonconservative force.
Conservative and Nonconservative Forces
Potential energy can
only be defined for
conservative forces.
Conservation of Energy
.
total energy:
Total energy conserved for a system that has no
non-conservative forces acting on it
Problem Solving Using Conservation of
Mechanical Energy
Problem Solving Using Conservation of
Mechanical Energy
If there is no friction, the speed of a roller
coaster will depend only on its height
compared to its starting height.
Problem Solving Using Conservation of
Mechanical Energy
For an elastic force, conservation of energy tells
us:
Power
Power is the rate at which work is done –
(6-17)
In the SI system, the units of
power are watts:
Ch. 7 Momentum & Impulse
Momentum and Its Relation to Force
Momentum is a vector symbolized by the
symbol p, and is defined as
The rate of change of momentum is equal to the
net force:
Conservation of Momentum
During a collision, total momentum does not
change:
Conservation of Momentum
The law of conservation of momentum states:
The total momentum of an isolated system of
objects remains constant.
Conservation of Momentum
Momentum conservation works for a rocket as
long as we consider the rocket and its fuel to
be one system, and account for the mass loss
of the rocket.
Collisions and Impulse
Impulse
= change in momentum
= average force X time
Conservation of Energy and Momentum in
Collisions
Momentum is conserved
in all collisions.
Collisions in which
kinetic energy is
conserved as well are
called elastic collisions,
and those in which it is
not are called inelastic.
Center of Gravity
The center of gravity can be found experimentally
by suspending an object from different points.
The CM need not be within the actual object – a
doughnut’s CM is in the center of the hole.
Ch. 8 Rotational Motion
Angular Quantities
Angular displacement:
The average rotational velocity
is defined as the total angular
displacement divided by time:
Angular Quantities
The rotational acceleration is the rate at which
the angular velocity changes with time:
Angular Quantities
Correspondence between linear and rotational
quantities:
Constant Angular Acceleration
The equations of motion for constant angular
acceleration are like those for linear motion:
Torque
The perpendicular distance from the axis of rotation
to the line along which the force acts is called the
lever arm.
Torque = Perpendicular Force X Lever Arm
Rotational Inertia
The quantity
is called the
rotational inertia of an object.
The distribution of mass matters here – these
two objects have the same mass, but the one on
the left has a greater rotational inertia, as so
much of its mass is far from the axis of rotation.
Rotational Inertia
The rotational inertia of
an object depends :
• Mass
•Shape
•Location of axis
Angular Momentum and Its Conservation
In analogy with linear momentum, we can define
angular momentum L:
Conservation:
If the net torque on an object is zero, the total
angular momentum is constant.
Angular Momentum and Its Conservation
Therefore, systems that can change their
rotational inertia through internal forces will also
change their rate of rotation:
Vector Nature of Angular Quantities
Vectors for rotational velocity & Angular
momentum:
• point along the axis of rotation
• direction is found using a right hand rule:
Ch. 9 Fluids
Density
The density ρ of an object is its mass per unit
volume:
Pressure in Fluids
Pressure is defined as the force per unit area.
the units are pascals:
1 Pa = 1 N/m2
Pressure is the same in every
direction in a fluid at a given
depth; if it were not, the fluid
would flow.
Pressure in Fluids
Also for a fluid at rest, there is no
component of force parallel to any
solid surface – once again, if there
were the fluid would flow.
Pascal’s Principle
If an external pressure is applied to a confined
fluid, the pressure at every point within the fluid
increases by that amount.
This principle is used in hydraulic lifts
Buoyancy and Archimedes’ Principle
For a floating object, the portion of the object
that is submerged displaces a mass of water
equal to the mass of the entire object.
Continuity of Flow
Bernoulli’s Principle
1 2
P  dv  constant
2
Lift on an airplane wing is due to the different
air speeds and pressures on the two surfaces
of the wing.
Ch. 10 Temperature & Heat
Heat As Energy Transfer
Heat is a form of energy.
1 cal is the amount of heat necessary to raise the
temperature of 1 g of water by 1 Celsius degree.
Definition of heat
Heat is energy transferred from one object to
another because of a difference in temperature.
Internal Energy
The total of all the energy of all the molecules in
a substance is its internal energy.
Temperature:
measures average kinetic energy of
molecules
Internal energy:
total energy of all molecules
Specific Heat
The amount of heat required
to change the temperature of
a material is proportional to:
• mass
• temperature change
• specific heat, c (a
material propert)
1Latent Heat
Energy is required for a material to change
phase, even though its temperature is not
changing.
Latent Heat
Heat of fusion, LF: heat required to change 1.0 kg
of material from solid to liquid
Heat of vaporization, LV: heat required to change
1.0 kg of material from liquid to vapor
Latent Heat
The total heat required for a phase change
depends on the total mass and the latent heat:
Heat Transfer: Convection
Convection occurs when heat flows by the mass
movement of molecules from one place to
another. It may be natural or forced; both these
examples are natural convection.
Heat Transfer: Radiation
The most familiar
example of radiation
is our own Sun,
which radiates at a
temperature of
almost 6000 K.
Summary p. 1
• In an isolated system, heat gained by one part
of the system must be lost by another.
• Calorimetry measures heat exchange
quantitatively.
• Phase changes require energy even though
the temperature does not change.
• Heat of fusion: amount of energy required to
melt 1 kg of material.
• Heat of vaporization: amount of energy
required to change 1 kg of material from liquid
to vapor.
Summary p. 2
• Heat transfer takes place by conduction,
convection, and radiation.
• In conduction, energy is transferred through the
collisions of molecules in the substance.
• In convection, bulk quantities of the substance
flow to areas of different temperature.
• Radiation is the transfer of energy by
electromagnetic waves.
Ch. 11 Thermodynamics
The First Law of Thermodynamics
The change in internal energy of a closed
system will be equal to the energy added to the
system minus the work done by the system on
its surroundings.
This is the law of conservation of energy,
written in a form useful to systems involving
heat transfer.
Isothermal process
An isothermal process is
one where the temperature
does not change.
In order for an isothermal process to take
place, heat flows from a hot body (heat
reservoir) to a cold body.
Adiabatic Processes
An adiabatic process is one where there is no
heat flow into or out of the system.
The Second Law of Thermodynamics
– Introduction
The process above doesn’t happen.
This tells us that conservation of energy (First
Law) is not the whole story. If it were, movies run
backwards would look perfectly normal to us!
The Second Law of Thermodynamics
– Introduction
The second law of thermodynamics is a
statement about which processes occur and
which do not. There are many ways to state the
second law; here is one:
Heat can flow spontaneously from a hot object
to a cold object; it will not flow spontaneously
from a cold object to a hot object.
15-5 Heat Engines
It is easy to produce thermal energy using
work, but how does one produce work using
thermal energy?
This is a heat engine;
mechanical energy can
be obtained from
thermal energy only
when heat can flow from
a higher temperature to
a lower temperature.
Heat Engines
We will discuss only engines that run in a
repeating cycle; the change in internal energy
over a cycle is zero, as the system returns to
its initial state.
The high temperature reservoir transfers an
amount of heat QH to the engine:
• part of it is transformed into work W
• the rest, QL, is exhausted to the lower
temperature reservoir.
Note that all three of these quantities are
positive.
Heat Engines
A steam engine is one type of heat engine.
Heat Engines
The efficiency of the heat engine is the ratio of
the work done to the heat input:
Heat Engines
The Carnot engine is idealized, as it has no
friction. Each leg of its cycle is reversible.
The Carnot cycle consists of:
• Isothermal expansion
• Adiabatic expansion
• Isothermal compression
• Adiabatic compression
Heat Engines
Heat Engines
Carnot engine efficiency is:
(15-5)
From this we see that 100% efficiency can be
achieved only if the cold reservoir is at absolute
zero, which is impossible.
Real engines have some frictional losses; the
best achieve 60-80% of the Carnot value of
efficiency.
Refrigerators, Air Conditioners, and Heat
Pumps
These appliances can be thought of as heat
engines operating in reverse.
By doing work, heat is
extracted from the cold
reservoir and exhausted to
the hot reservoir.
Refrigerators, Air Conditioners, and Heat
Pumps
Refrigerators, Air Conditioners, and Heat
Pumps
A heat pump is like an air conditioner turned
around, so that the coils dump heat inside the
house:
Entropy and the Second Law of
Thermodynamics
Another statement of the second law of
thermodynamics:
The total entropy of an isolated system never
decreases.
Order to Disorder
Entropy is a measure of the disorder of a
system. This gives us yet another statement of
the second law:
Natural processes tend to move toward a state
of greater disorder.
Example: If you put milk and sugar in your
coffee and stir it, you wind up with coffee that
is uniformly milky and sweet. No amount of
stirring will get the milk and sugar to come
back out of solution.