Herriman High Honors Physics Chapter 5 Work, Power and Energy What You Need to Know

Herriman High Honors Physics

Chapter 5Work, Power and Energy

What You Need to Know


Energy Facts There are different types of energy Energy of all types is measured in

Joules Law of Conservation of Energy –

Energy can be neither created nor destroyed, merely changed from one form to another


Types of Energy(Unit Overview)

Mechanical Potential Energy Energy of Position

Gravitational Elastic

Kinetic Energy Energy of Motion

If it moves it has kinetic energy Heat Energy

Heat is a form of Energy Transfer Other Forms of Stored Energy

Chemical Fuels - usually release energy by combusion Food – energy released by digestion

Electrical Generated from other forms of energy


Work The Physics definition of work requires

a displacement, i.e. an object must be moved in order for work to be done!

The Applied force which causes the displacement contributes to the work, i.e. in order to contribute to the work, the applied force must be parallel to the displacement.


Work: A Mathematical Definition

Work = (Force)(Displacement) Units of Work = (Newton)(Meter) 1 Newton•Meter = 1 Joule A Joule is a unit of Energy and it

takes energy to do work and work done on an object either causes it to move (kinetic energy) or is stored (potential energy)


Work done Parallel to the Applied Force

Sample Problem

What work is done sliding a 200 Newton box across the room if the frictional force is 160 Newtons and the room is 5 meters wide?

W = Ff • ΔX = (160 N)(5 m)

800 Joules


Work (Not Parallel to the Applied

Force)Sample Problem

How much work is done on a vaccum cleaner pulled 3.0 meters by a force of 50 N at an angle of 30° above the horizontal?

Solve Given:

F = 50 N θ = 30° Δx = 3 m

Find W W = F cos θ (Δx) = (50 N)(cos 30°)(3 m)

= 130 Joules Try: p. 162

Practice A

Problems 1 & 3


Kinetic Energy Kinetic Energy is energy of Motion

Any moving object has kinetic energy Dependent on the mass of the object

and its velocity. Mathematically expressed as:

Ek = ½ mv2


Sample Problem What is the kinetic energy of a car

with a mass of 2000 kg moving at 30 m/s?

Ek = ½ mv2 = (½)(2000 kg)(30 m/s)2

= 900,000 Joules

Try: p. 166

Practice B

Problems 1, 3 & 5


Work – Energy Theorem The net work done on a body

equals its change in kinetic energy. Mathematically:

Wnet= ΔKE Net work = change in kinetic energy


Work-Energy TheoremSample Problem

On a frozen pont, a person kicks a 10 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

Try: p. 168

Practice C

Problems 2 & 4


Energy of Position:Gravitational Potential

Energy Occurs due to the accelerating force of

gravity Is determined by the position of the

object in the gravitational field Is a form of stored energy Mathematically determined by: PEg =

mgh where m is mass, g is the acceleration due to gravity and h is the height above a determined baseline.


Sample Problem What is the potential energy of a

10 kg rock sitting on a cliff 30 meters high? The acceleration due to gravity is 9.8 m/s2.

Ep = mgh = (10 kg)(9.8 m/s2)(30 m)

2940 Joules


Elastic Potential Energy Bungee cords, rubber bands, springs

any object that has elasticity can store potential energy.

Each of these objects has a rest or “zero potential” position When work is done to stretch or

compress the object to a different position elastic potential energy is stored


Elastic Potential Energy

Top picture is “rest position”; x = 0 This is a point where the elastic potential energy = 0

Bottom picture is “stretched position” Here elastic potential energy is stored in the spring PEelastic = ½ kx2 where k is the “spring constant” in

N/m


Sample Problem What is the Elastic potential

energy of a car spring that has been stretched 0.5 meters? The spring constant for the car spring is 90 N/m.

PEelastic = ½ kx2 = (½)(90 N/m)(0.5 m)2

=11.25 Joules


Where Does “K” Come From?

K is measured in Newtons/meter. It is defined as the force required to displace a spring 1 meter. So:

K = F/x Often K is determined by hanging

a known weight from the spring and measuring how much it is stretched from its rest postion.


Sample Problem A spring is hung from a hook and a 10

Newton weight is hung from the spring. The spring stretches 0.25 meters.

What is the spring constant? If this spring were compressed 0.5

meters, how much energy would be stored?

If this spring were used to power a projectile launcher, which fires a 0.2 kg projectile, with what velocity would the projectile leave the launcher? Assume 0.5 m compression.


SolutionK = F/x

K =10 N/0.25 m = 40 N/m

Ep = ½ Kx2

Ep = ½ (40 N/m)(0.5 m)2 = 5 Joules

Ep = Ek = ½ mv2

5 Joules = ½ (0.2 kg)(v2)V = 7.05 m/s Try: p. 172

Practice D

Problems 1 & 3


Conservation of Energy To say something is conserved is to say

that it stays the same. In the absence of friction, mechanical

energy (kinetic, gravitational, elastic) is always conserved.

Mathematically: MEi = MEf

Most commonly we talk about a combination of kinetic and gravitational energies so this becomes:

ffii mghmvmghmv 22

2

1

2

1


Conservation of EnergySample Problem

Starting from rest a child zooms down a frictionless slide from an initial height of 3 meters. What is her speed at the bottom of the slide? Assume she has a mass of 25 kg.

Answer: 7.67 m/s

Try: p. 177

Practice E

Problems 1, 3 & 5


Power Power = Work/time = Joules/Second

= watt Mathematically there are two

formulas for Power:

tdF

P or since FVP v

td

then


PowerSample Problem

A 193 kg curtain needs to be raised 7.5 meters at a constant speed, in as close to 5 seconds as possible. The power ratings for three motors as listed as 1 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job?

Given: M = 193 kg T = 5 sec Δx = 7.5 meters

So: P = W/t = FΔx/t = mgΔx/t Substituting: P = (193 kg)(9.8 m/s2)(7.5 m)/5 sec

= 2.8 kW Which means that the 3.5 kW motor is best for

the jobTry: p. 181

Practice F

Problems 2 & 4

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Herriman High Honors Physics Chapter 5 Work, Power and Energy What You Need to Know