Work… In everyday speech work has a very general meaning. In describing motion in physics, work has a very specific meaning.

No work is done on the chair Chair Example Standing Walking No work is done on the chair

Work is defined as the product of the force applied to cause motion and the distance the object moves in the direction of the force. Work is done only when components of a force are parallel to a displacement

FORMULA W = fd IN DIRECTION OF MOTION The symbol for work is W Work has 2 acceptable units Nm Joules (J)

JOULE Lifting an apple about 2ft is a Joule 3 good push-ups is about 1000J

Situations that affect the sign of work Force is in the direction of motion Positive Work Force opposes motion Negative Work Force is 90° to motion No Work Object is not in motion No Work

Notice direction of motion is the same as the applied force W = fd W = 20J of Work 10N Moves 2m Notice direction of motion is the same as the applied force

How would you solve this How would you solve this? Force applied is NOT in the same direction as the objects motion. 10N Y 60° X 2m Think back to vectors and use the component of the force applied in the direction the object moves.

COS 60° = force parallel to motion COS θ = adj/ hyp COS 60° = force parallel to motion 10N 10N force para. = COS 60° (10N) force para. = 5N Y 60° X 2m w = F(parallel) D 5N (2m) = 10Nm

W = Fd (COS θ) θ = 0° θ = 90° Always measure angle with horizontal! The above formula works in every case θ = 0° No work because no motion in direction of force θ = 90°

Pg. 170 Problems 1-4

Section Review p. 171 With your Neighbor, answer questions 2, 3, 4

Section Review Answers 2 the neighbor, twice as much 3 a-negative B-positive C- negative 4 a-yes B- no C-yes

The Stuff that makes things move Energy The Stuff that makes things move The ability to do work Has the units of Joules (J) There are 2 kinds of mechanical energy

Kinetic Energy KE = ½ mV2 manipulated V = 2KE/m M = 2KE/V2 This is the energy associated with an objects motion. KE depends on mass and velocity When the object is treated as a particle, the formula for KE is… KE = ½ mV2 manipulated V = 2KE/m M = 2KE/V2

KE is a scalar quantity The SI unit for KE is the Joule, yes the same as for work Look at sample prob. 5B Page 173 DO practice problems 5B 1-5 on page 174

Work- Kinetic Energy Theorem The net work done on an object is equal to the change in the kinetic energy of the object Wnet = ΔKE Wnet = KEfinal – KEinitial fd(cos θ) = ½ mV2 The KE of an object is equal to the work that moving object can do

This theorem allows us to think of KE as the work an object can do as it comes to rest, or the amount of energy contained in the moving object The KE of the moving hammer can do work KE = Work done (net) fd = ½ mv2 some of the energy is sound, heat and light (if spark)

Practice Problems 5C p.176 #1 and 4 only

Potential Energy This is the energy associated with an object due to the position of the object. STORED ENERGY There are two kinds of potential energy GRAVITATIONAL POTENTIAL ENERGY ELASTIC POTENTIAL ENERGY

Gravitational Potential Energy (PEg) The energy associated with an object due to the objects position relative to a gravitational reference Wh = PEg = mgh = mass x gravity x height acceleration gm = w Has the unit of joules

Elastic Potential Energy (PEelastic) The energy associated with a stretched or compressed elastic object Spring, bungee cord, rubber band

Elastic Potential Energy

Practice Problems 5D 1-3 pg. 180 Overhead (springs) In both the compressed and stretched example, energy is stored PEelastic = ½ KX2 K = spring constant X = distance stretched or compressed Practice Problems 5D 1-3 pg. 180

Conservation of Energy To say something is conserved is to say it remains constant. Something can change form and still be conserved. burning log: matter and energy are conserved. smoke water vapor gas ASH 5Kg 5Kg

Pendulum Energy is transferred from one form to another As the pendulum swings, PE is transferred to KE. As the bob swings upwards KE is stored as PE PE = max KE = min PE = max KE = min PE = min KE = max

A falling egg PE = 10 J KE = 0 J PE = 5 J KE = 5 J PE = 0 J KE = 10 J Mass = .1kg Height = 10m PE = 10 J KE = 0 J PE = mgh PE = 5 J KE = 5 J 10M PE = 0 J KE = 10 J

Mechanical Energy The sum of Kinetic Energy and ALL forms of Potential energy associated with an object or group of objects ME is not a unique form of energy. Its merely a way of classifying energy ME includes KE and PE

Mechanical Energy Σ SPN ME is different from non mechanical energy (nuclear, chemical, thermal, internal, electrical) ME = Σ KE + Σ PE ME = ½ mv2 + mgh (if PE is NOT present, elastic) Σ SPN

Conservation Of Mechanical Energy Conservation of Mechanical Energy can also be written as… MEi = MEf ½ mvi2 + mghi = ½ mvf2 + mghf True when friction can be ignored

The Law of Conservation of Energy: The total energy of a closed system is constant. Notice: The total energy of the system remains constant. Energy just simply changes from KE to GPE and back and forth again. GPE-relates to height KE- relates to speed 33

Often is the case that KEi or KEf or PEi or PEf will be zero Often is the case that KEi or KEf or PEi or PEf will be zero. When that is the case… mgh = ½ mv2 2mgh = v2 m V = 2gh h = V2 2g

28-31, 33, 34a Look at sample problem 5E Practice problems 5E #s 5,2,1 Problems p.185 Look at sample problem 5E Practice problems 5E #s 5,2,1 HOMEWORK!! 28-31, 33, 34a All on page 195 of packet

Power This quantity also has a very specific meaning in science that can be confused by common English usage Power is the rate of doing work That is to say that power is the rate at which energy is transferred

Power Power is work done divided by the time taken to do the work Power = Work = fd P = w Time t t Power is measured in watts (W) J/s A watt is a small unit, 1 watt is about what is needed to lift a 2N glass of water .5m to your mouth in 1 second.

Watts Since watts are so small, we sometimes use Kilowatts 1 KW = 1000W Watts are metric Horse power is traditional 1 Horse power = 746 Watts

Watts Watts are named after James Watt, the inventor of the steam engine

Practice Problem An electric motor lifts an elevator that weighs 12000N a distance of 9m in 15sec What is the motors power in watts? What is the motors power in kilowatts? Given f = 12000N d = 9m t = 15s P = ? Formula P = fd/t Solution P = 12000(9) 15 P = 7200 W 7.2 KW

Sample Problem p. 188 Pg. 189 5F 5, 4, 3, 2