Work, Energy and Power

Chapter 5 Section 4

Wagon Example

Push a wagon on a sidewalk and it starts to roll down the sidewalk.

The wagon eventually comes to a stop shortly after the push.Friction slows the wagon down.

Mechanical Energy is not conserved in the wagon since there is a change in kinetic energy.

Work-Kinetic Energy Theorem

Work-Kinetic Energy Theorem – The net work done on an object is equal to the change in the kinetic energy of the object.

Work-Kinetic Energy Theorem Equation

Wnet = ΔKE

Wnet = Net WorkΔKE = Change in kinetic Energy

Force is not required and applies to all objects universally.

Friction

When dealing with the work done by friction, the Work-Kinetic Energy Theorem can be put into an alternative form.

Wfriction = ΔME

Frictionless

When a problem deals with frictionless objects or where friction is neglected.Wfriction = 0ΔME = 0MEi = MEf

This is the Conservation of Mechanical Energy

Work-Kinetic Energy Theorem & Work

It doesn’t matter if friction is present or its frictionless, the Theorem demonstrates that work is a method of transferring energy.

Perpendicular forces to the displacement cause no work, cause the energy is not transferred.

Distinction Between W and Wnet

Its important to make the distinction between the two expressions:W = Fd(cosθ)

This expression applies to the work done on an object due to another object

Definition of workWnet = ΔKE

Shows only the NET FORCE on an objectRelates to the net work done on an object to

change the kinetic energy of an object

Example Problem

A 10.0 kg shopping cart is pushed from rest by a 250.0 N force against a 50.0 N friction force over a 10.0 meter distance.

1. How much work is done by each force on the cart?

2. How much kinetic energy has the cart gained?

3. What is the cart’s final speed?

Example Problem Answers

1. 2500 J2. 2000 J3. 20 m/s

Everyday Power

What is power?A few everyday uses of power.

ElectricityEnginesEtc…

Basically any time work is done, power is generated.

Power

Power – The rate at which energy is transferred.

In other words, power is the rate at which energy is transferred.

What is Power?

Power is the amount of work done over a certain time interval.

P = W/t

P = Power (watt)W = Work (J)t = Time (s)

Alternative Power Form

Power can also be described through forces and the speed of the object.

P = Fv

Power = Force • Speed

SI Units of Power

The SI units for Power is the “watt”A watt is equal to one joule or energy

per second

Horsepower is often used with power when dealing with mechanical devices such as engines.1 horsepower = 746 watts

Road Design

Why are many mountain roads built so that they zigzag up the mountain rather than straight up?

The Physics Behind Road Design

The same energy is needed to reach the top of the mountain regardless of the path.Therefore the work is the same.

The zigzag path has a longer distance and takes more time to reach the topTherefore less power is needed on the

zigzag path vs. straight up.

Machine Power

Machines with different power ratings do the same work, but do so over different time intervals.

The only main difference between different power motors is that more powerful motors can do the work in a shorter time interval.

Example Problem

Two horses pull a cart. Each horse exerts a 250.0 N force at a 2 m/s speed for 10.0 minutes.

1. Calculate the power delivered by the horses.

2. How much work is done by the two horses?

Example Problem Answers

1. 1000W or 1kW2. 600,000 Joules or 0.60MJ

Light Bulbs

A common everyday thing that you take for granite is artificial light.A light bulb usually has marked on it the

wattage it uses.Example: 60 watt light bulb (most common)A 60 watt light bulb will use 60 joules of

energy over the course of 1 second.Where does the energy come from?

From Sunlight to Artificial Light

Sunlight Plants Fossil Fuel (coal) Steam Turbine Electricity Light

Whenever energy is transferred, heat is produced.2nd Law of Thermodynamics

So it takes light to produce light and its very inefficient.