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)