Energy

Chapter 8: Physics Matters(By James Trefil and Robert Hazen)

Some initial questions

What does it mean to do work?

Can you do a work out without ever actually doing any work?

Why is it dangerous to speed/tailgate when driving a car?

Other questions we will eventually be able to answer!

How come a ball never bounces as high as it was dropped?

Why does the roller coaster work without a motor on the car?

Work

Work is done whenever a force is exerted on an object over a distance

- It is the transfer of energy that results in moving an object over a distance.

Work = Force x DistanceN m

Newton-meters are known as “Joules” (J)

dFW

Work

How much work do you to to lift a 5 kg book from the floor onto a table if the table is 3m high?

How far will you lift a 20N bag if you do 100 J of work on it?

Work and Energy

When you do work you transfer energy or use energy.

-Energy is a system’s ability to do work

-Since work is measured in Joules and work is a transfer of energy, energy must also be measured in Joules.

There are many different forms of energy, what are they?

Is this Work?

Power

Power is the rate at which energy is used, or the rate at which work is done.

- The faster energy is used or transferred, or the faster work is done on an object, the more power that is expended by the machine doing the work.

t

W

time

Work

time

EnergyPower

PowerFor what everyday things do we tend to pay attention to power?

One major type of thing are the bulbs that light our rooms. How do we differentiate between different types of bulbs?

Watts! Wattage is a unit of measurement that tells us how much energy the bulb will use in a certain amount of time.

Power is measured in Watts (joules per second).

- So, a more powerful bulb will use stored energy faster then a weaker bulb with the same amount of stored energy.

HorsepowerThe English system form of power was based on how much a single horse can pull.

This was known as horsepower!

1 horsepower 746 Watts

A space shuttle has over 37 million horsepower!

PowerHow powerful is an elevator that can lift a mass of 400kg up a building of height 100 m in 20 seconds?

Question

Lindsey wants to hike up this 400 m mountain and she has a mass of 48 kg. If she takes the path that you see and hikes a distance of 620 m, how much work does she do against gravity to get up the mountain?

Does Andi, who has the same mass as Lindsey, do more or less work if instead of hiking, she rock climbs up a sheer cliff strait up to the pinnacle?

Question Continued

Who is more powerful if Lindsey takes 3 hours to hike the path, but Andi, being a professional rock climber (maybe I should have said Maggie), takes only an hour to scale the cliff?

Hmmmmmm

When both Lindsey and Andi each reach the top of the mountain, do they have any energy left?

Yes! But what type of energy to do they have?

Potential Energy

• Basically it is energy stored in a system

Both girls have what is called “Gravitational Potential Energy.”

•Since gravity could exert a force on either of them to make them fall to the ground from the top of the mountain, there is potential for work to be done on them, and hence, potential energy.

Gravitational Potential Energy:

mghPE Which is mass x acceleration due to gravity x height

Potential Energy

How much potential energy does each girl have?

Gravitational Potential Energy

• Independent of Path to get there

Kinetic EnergyIf Philip is waiting at the top of the mountain to show Lindsey the awesome new set of wings he built, and he has a mass of 55 kg, how much potential energy does he have?

Can he convert his potential energy into anything?

Yes! If he jumps off the cliff, gravity will do work to pull him toward the ground, converting his potential energy into kinetic energy.

Kinetic EnergyKinetic Energy is the energy an object has because it is moving.

It is similar to momentum as they both result from the movement of masses, but they differ in the fact that KE is a scalar quantity.

Also, as velocity increase, momentum also increases linearly, but KE increases as a squared function (if v goes up by 2, KE goes up by 4)

2

2

1mvKE

Kinetic Energy

How much Kinetic Energy will Philip have as he hits the ground, if he jumps of the mountain at the sheer cliff face, and his new wings fail completely?

Notice any Coincidences?

Conservation of Energy

Just like with momentum, the total energy of a system is never lost… It is conserved!

This means, that in the case of Philip jumping off a mountain, he converted his Potential Energy at the top of the mountain completely into Kinetic Energy by the time he reached the ground.

If energy is always conserved, why wont our experiments always work?

Conservation of EnergyIf this cliff is 150 m high, and the person in the picture has a mass of 65 kg, how much PE does he have at the top of the cliff? How much KE does he have at the top of the cliff?

How much KE does he have as he hits the water? How much PE does he have?

How much PE and KE does he have half way down the cliff?

Conservation of Energy

What is his velocity as he hits the water?

Conservation Equation

KEPEET

The total energy in a system is equal to the sum of the potential energy

and the kinetic energy at any given time.

Conservation of EnergyThis means that when something falls from a height, its initial potential energy is equal to its final kinetic energy.

-As an object falls, it is speeding up but losing height. Therefore, it is gaining kinetic energy at the same rate that it is losing potential energy.

-In fact, gravity is doing work on the object to convert its PE into KE!

Conservation of Energy

maxmax KEPE

There are two more important things to realize.

For a given system:

AND

When PE is at its maximum, KE is at its minimum, and when KE

is at its maximum, PE is at its minimum.

The Work-Energy Theorem

The work done on an object is equal to the combination of the changes in both kinetic and potential energy.

Spring Potential

Just like how increasing the height of an object will store potential

energy in the object based on how much gravity might be able to move

it, elastic things can also store potential energy. This is known as

Elastic Potential Energy.