Advanced Physics
Chapter 6Work and Energy
Work and Energy
6-1 Work done by a Constant Force 6-2 Work done by a Varying Force 6-3 Kinetic Energy, and the Work-Energy Principle 6-4 Potential Energy 6-5 Conservative and Nonconservative Forces 6-6 Mechanical Energy and Its Conservation 6-7 Problems Solving Using Conservation of Mechanical
Energy 6-8 Other Forms of Energy 6-9 Energy Conservation with Dissipative Forces: Solving
Problems 6-10 Power
6-1 Work done by a Constant ForceWork Describes what is accomplished by the
action of a force when it acts on an object as the object moves through a distance
The transfer of energy by mechanical means The product of displacement times the
component of the force parallel to the displacement
Both work and energy are scalar quantities
6-1 Work done by a Constant Force
Work
W = Fd Or
W = Fd cos where is the angle between the
direction of the applied force and the direction of displacement
6-1 Work done by a Constant Force
Work
W = Fd cos Force
Displacement
6-1 Work done by a Constant Force
Work Units: joule (N•m) 1 joule = 0.7376 ft•lb
6-1 Work done by a Constant Force
Work Negative work? What about friction? Work done on Moon by Earth? Work done by gravity depends only
on height of hill not incline angle.
6-2 Work done by a Varying Force Work done by a variable force in moving
an object between 2 points is equal to the area under the curve of a Force (parallel) vs. displacement graph between the two points.
Why? Or we will have to do some calculus on it!
6-2 Work done by a Varying Force
Force vs. Distance
0
5
10
15
20
25
0 5 10 15
Distance (m)
Fo
rce (
N)
Series1
6-3 Kinetic Energy, and the Work-Energy Principle
Energy The ability to do work (and work is?)Kinetic Energy Energy of motion; a moving object
has the ability to do workTranslational Kinetic Energy (TKE) Energy of an object moving with
translational motion (?)
6-3 Kinetic Energy, and the Work-Energy Principle
Translational Kinetic Energy (KE)
KE = ½ mv2
6-3 Kinetic Energy, and the Work-Energy Principle
Work-Energy Principle The net work done on an object is
equal to the change in its kinetic energy
Wnet = Kef – Kei = KE TKE m and v2 But…what about potential
energy????
6-4 Potential Energy
Potential Energy Energy associated with forces that
depend on the position or configuration of a body (or bodies) and the surroundings
Gravitational Potential Energy Potential energy due to the position
of an object relative to another object (gravity)
6-4 Potential Energy
Gravitational Potential Energy Potential energy due to the position
of an object relative to another object (gravity)
PEgrav = mgy
6-4 Potential Energy
Potential Energy In general the change in potential
energy associated with a particular force is equal to the negative of the work done by the force if the object is moved from one point to another.
W = -PE
6-4 Potential EnergyElastic Potential Energy Potential energy stored in an object that
is released as kinetic energy when the object undergoes a change in form or shape
For a spring:
Elastic PE = ½ kx2
Where k is the spring constant
6-4 Potential Energy
Elastic Potential Energy For a spring: The force that the spring exerts when it is
pushed or pulled is called the restoring force (Fs) and is related to the stiffness of the spring (spring constant-k) and the distance it is compressed or expanded
Fs = -kx
6-4 Potential Energy
Elastic Potential Energy For a spring:
Fs = -kx This equation is called the spring
equation or Hooke’s Law
6-5 Conservative and Nonconservative Forces
Conservative Forces Forces for which the work done by the
force does not depend on the path taken, only upon the initial and final positions.
Examples: Gravitational Elastic Electric
6-5 Conservative and Nonconservative Forces
Nonconservative Forces Forces for which the work done
depends on the path takenExamples: Friction Air resistance Tension in a cord Motor or rocket propulsion Push or pull by a person
6-5 Conservative and Nonconservative Forces
Work-Energy Principle (final) The work done by the
nonconservative forces acting on a object is equal to the total change in kinetic and potential energy.
Wnc = KE + PE
6-6 Mechanical Energy and Its Conservation
Total Mechanical Energy (E)
E = KE + PE
6-6 Mechanical Energy and Its Conservation
Principle of Conservation of Mechanical Energy
If only conservative forces are acting, the total mechanical energy of a system neither increase nor decreases in any process. It stays constant—it is conserved
KE1 + PE1 = KE2 + PE2
KE = -PE
6-7 Problems Solving Using Conservation of Mechanical Energy
E = KE + PE = 1/2mv2 + mgyKE = -PE 1/2mv2
1 + mgy1 = 1/2mv22 +
mgy2
Sample problems: P.160 – 165
6-8 Other Forms of EnergyOther Forms of Energy: According to atomic theory, all types of
energy is a form of kinetic or potential energy.Electric energy Energy stored in particles due to their charge KE or PE?Nuclear energy Energy that holds the nucleus of an atom
together KE or PE?
6-8 Other Forms of EnergyOther Forms of Energy:Thermal energy Energy of moving (atomic/molecular)
particles KE or PE?Chemical energy Energy stored in the bonds between
atoms in a compound (ionic or covalent) KE or PE?
6-8 Law of Conservation of EnergyLaw of Conservation of Energy The total energy is neither increased nor
decreased in any process. Energy can be transformed from one form
to another, and transferred from one body to another, but the total remains constant
This is one of the most important principles in physics!
6-9 Energy Conservation with Dissipative Forces: Solving Problems
Dissipative Forces Forces that reduce the total
mechanical energyExamples: Friction Thermal energy
6-9 Energy Conservation with Dissipative Forces: Solving Problems
Problem Solving (Conservation of Energy) Draw a diagram Label knows (before/after) and knowns
(before/after) If no friction (nonconservative forces) then…
KE1 + PE1 = KE2 + PE2
If there’s friction (nonconservative forces) then add into equation
Solve for the unknown
6-10 Power
Power The rate at which work is done The rate at which energy is
transferred Units (what?) 1W = 1J/s 746 W = 1 hp
6-10 Power
Power
P = W/t = Fd/t P = F v (since v =d/t)