Lesson 5-1Definition of Work

Definition of Work

So far, many of the terms we have discussed have had similar scientific and real world definitions

Usually when we say ‘work’, we think of doing something that requires physical or mental effort

In Physics, work is very different

Definition of Work

Consider the following: A student holds a book at arms length for several

minutes A student carries a bucket of water along a

horizontal path

Even though work is required for both of these actions, no work is done on the book or the bucket

Definition of Work

Only when a force displaces an object is work done on the object Imagine your car runs out of gas If you push your car with a constant force to the

gas station, you are doing work on your car Work is equal to the applied force times the length

of distance the force is applied

W=Fd

Definition of Work

Work is not done on an object unless the object is moved by a force That is why no work is done on the book in our

previous example No work is done because the book is stationary

That is why no work is done on the chair in our previous example Work is done within the body to move, but none on the

chair

Work

Work is done ONLY when components of a force are parallel to a displacement When application of force and displacement are in

different directions, only the parallel component of force to the displacement does work Perpendicular forces do no work

Parallel Forces Do Work

Imagine pushing a crate across the floor If you get very low, almost laying on the ground,

and push exactly horizontally All of your force will go into moving the crate

If you push at an angle, only your horizontal component will help move the crate The vertical component ‘drives’ the crate into the

ground and does no work to help you move the crate

Only forces parallel to the displacement do work

Units of Work

The SI unit of work is the Joule Joules = Force times length =Newton Meters

Sample pg 169 Practice pg 170

Sign on Work

Work is a scalar quantity and can be positive or negative Work is positive when the component force is in

the same direction as the displacement Lifting a box, force and displacement in the same

direction Work is negative when the component force is in

the opposite direction as the displacement The force of friction between a sliding box and the

floor

Sign on Work

If you carried a box into the next room, what would be the sign on the work done on the box? Since no work is done, sign does not matter, its

like asking “What is the sign on zero?”

Sign on Work

Work may result in a change in velocity If the work is in the same direction as the

displacement, how will the velocity change? Increase

If work is in the opposite direction, how will the velocity change? Decrease

Lesson 5-2Energy

Kinetic Energy (KE)

Kinetic Energy is energy associated with motion

Kinetic Energy depends on the speed of an object As an object’s speed increases, the object’s KE

increases

KE

If a bowling ball and a volley ball are rolling at the same speed, which has more KE? You may think that they have the same amount

since they are traveling at the same speed

KE depends on speed and mass

KE mv= 1

22

KE

KE is a scalar quantity The SI unit is the Joule, just like work

As per the KE/Work theorem, work is a type of energy

Sample pg 173 Practice pg 173

Potential Energy (PE)

A perfect example of energy is the ‘Skycoaster’ at Kennywood.

When the riders are at the top, they are not moving, so they have no KE. Recall, energy cannot be created or destroyed, so

the KE must go somewhere while the riders are stationary at the top

We explain the lack of KE as Potential Energy

PE

Potential energy is concerned with the position of the object, not the speed

PE is stored energy Describes an object’s potential to move based on

its relationship to another location

Gravitational PE

Gravitational PE depends on height from a zero level The energy associated with an object due to the object’s

position relative to a gravitational source is Gravitational PE

If a ball falls off of a table, it gains speed. From where does the speed come?

SI unit for PE is also the Joule

PE mghg =

Gravitational PE

This concept is valid only when free-fall acceleration is constant, such as near the Earth’s surface

Gravitational PE depends on both height and free fall acceleration, neither of which are properties of an object

For that reason, PE of an object is relative

Gravitational PE

For instance, lets say a ball is dropped from a second story roof and lands on a first story roof If PE was measured from the ground, PE is NOT

now zero If PE was measured from the first story roof, PE

IS now zero Is it possible to have a negative PE? Is it possible for the same object to have both positive

and negative PE at the same time?

Gravitational PE

The zero level is the level where PE = 0 It can be chosen specific for each situation The zero level should be chosen carefully so

as to make the most sense for the specific situation

Elastic PE

Another type of PE is that of elasticity Depends on the compression or stretching of an

elastic object

Examples? Imagine a pinball machine

The plunger is pulled back, compressing a spring When released, the plunger flies forward and

propels the ball The ball travels because of the stored PE in the spring

Elastic PE

When a spring is not compressed or stretched, it is said to be in a relaxed state or relaxed length

When external forces compress or stretch the spring, the spring stores PE

When the spring is released, the PE is converted to KE The amount of PE is directly related to the

amount the spring was stretched or compressed

Hooke’s Law

Named after British Physicist Robert Hooke

Mathematically approximates the PEelastic of a spring

PE kxelastic = 1

22

The Spring Constant

The symbol k is called the spring constant For a flexible spring, k is small For a more rigid spring, k may be huge The spring constant is measured in N/m

You will either be given k or asked to solve for k. You are not expected to just ‘know’ what k is.

Mechanical Energy

Descriptions of motion of many objects involves a more complete energy approach For example, think of a clock with a pendulum While the pendulum swings, it is constantly

converting PE into KE and KE into PE Also, there is elastic PE from the many springs

helping to power the clock

Mechanical Energy

The expressions of these energies are relatively simple

Energies such as nuclear and chemical are not so simple, but often they can be ignored because they are not directly relevant to the situation being analyzed

Mechanical Energy

Mechanical energy is the total sum of kinetic and potential energies associated with an object or group of objects

Energy that is not mechanical is called non-mechanical energy

ME KE PE= + ∑

Lesson 5-3Conservation of

Energy

Conserved Quantities

When we say something is conserved we mean that is remains constant That does not mean the quantity cannot change

forms during that time

But if at any given time, if we consider all forms of the quantity, we will have the same amount at all times.

An example of a conserved quantity is mass

Conservation of Energy

Energy cannot be created nor destroyed That is to say, energy is always conserved

But when we drop a ball, the ball does not return the original height. Why not? Energy is lost through friction, sounds, heat

Conservation of Energy

If we ignore these outside types of energy, we see that mechanical energy is totally conserved

ME MEi f=

ME KE PE= +

KE mv= 1

22PE mgh= and

Conservation of Energy

If we make the final equivalent substitutions, we see that mechanical energy is mathematically:

1

2

1

22 2mv mgh mv mghi i f f+ = +

Conservation of Energy

Notice that mass shows in every term Recall: all objects fall at the same rate no matter

their mass Do you need to know the mass to work this equation?

Sample pg 181 Practice pg 182

Lesson 5-4Work, Energy, and

Power

The Work – KE Theorem

Imagine sliding a hockey puck across the ice We know there exists a small amount of Fk

The puck slows and eventually stops

We also know from our study of energy that mechanical energy is not totally conserved

There is a relationship between the energy lost and the work done to an object

The Work – KE Theorem

The Work – KE Theorem is defined as

Notice the type of force is not specified because it could be any force working on any object The theorem is universal for all objects

W KEnet = ∆

Extension of the Work – KE Thm.

The extension of the theorem is useful when work is done by friction

If there is no friction then: The equation can be simplified

W MEfriction = ∆

∆ME = 0ME MEi f=

Work – KE Theorem

Notice the Work – KE Theorem in any form is a method of transferring energy

Recall that a force perpendicular to displacement does no work The force must be parallel to the displacement for

work to be done

If the force is perpendicular, and no work is done No energy is transferred

Distinction Between Equations

Is the work done by an object on another object

Relates net work done on an object to the change in KE

Sample 185 Practice 186

W Fd= (cos )θ

W KEnet = ∆

Power

The rate at which work is done is called power Power is the rate of energy transferred by any

method

PW

t=

∆

Power

We may also rewrite the equation substituting the definition of work

Therefore:

W Fd= P Fd

t=

∆

d

tv

∆=

P Fv=

, and

, and recall

Unit of Power

The SI unit of Power is the Watt Watts are most common in light bulbs

A dim light bulb may require 40 W to power it A bright light bulb may require 500 W to power it

Horsepower is also a unit of power 1 HP = 746 W = 746 J/s

Sample 188 Sample 188 Explanation Practice 188