Work & Energy

In the past…

v, a, x, t How things move, Kinematics F, a, m What makes them move, Dynamics

Now we will look at WHY they move!!! Energy!

Energy The ability to do work.

The theme of this unit is:Energy is Energy is Energy

Color Code for this power point: • Energy words will appear in red.

• Forces will appear in yellow.

• Distances will appear in green.

Work = Force x Distance W = F x d

In units this means

1 Joule = 1 Newton x 1 Meter

Joule (J) is pronounced (jewel) and is the unit for Work (W) of any kind.

W = F x d

Newton (N) is the unit for Force (F) and

W = F x d

Meter is the unit for distance.

W = F x d

For Work (W) to take place on any object

1. There must be a force (F)

2. The object must travel a distance (d).

• Anything that puts a force on an object displacing it will cause work.

Positive energy is + if it is going into the object/system

Negative energy is – if it is coming out of the object/system

Which of the following do work on the box?

gravity No. Doesn’t move up or down

normal force

you pulling it

friction Yes, it opposes the motion.

No. Doesn’t move up or down

Yes, but only the x direction.

Example Problem:

How much work will the road do on 18,000 N car when its brakes are applied, if the car

skids 10 m?

W = F x d

W = 18000 N x 10 m

W = 180,000 J

Which force is at work? Friction because it is

opposing motion.

Law of Conservation of Energy Energy cannot be created or destroyed

It can only change form.

There are many forms of energy.

We will study four types.

1.Work

2.Gravitational Potential Energy

3.Kinetic Energy

4.Elastic Potential Energy

Work: must be a force and distance W = F x d

Gravitational Potential Energy: Energy due to position. Must be a height

off the ground, gravity, and mass.

GPE = m x g x h

Kinetic Energy: Energy due to motion. Must have velocity and mass.

KE = ½ mv2

The fourth type is called Elastic Potential Energy

because it is energy due to springs or rubber bands.

We will focus on springs for this lesson.

So SPE means Spring Potential Energy.

SPE requires obviously a spring and how strong it is.

This is represented by little letter k in a formula.

SPE also requires a measure of how far a spring is

stretched or how far it is pushed together.

SPE = (1/2) k x2

Conservation of Energy

Now that you know four types of energy and the theme is

Energy is Energy is Energy

That means

Work = KE= GPE = SPE

F x d = ½(mv2 ) = m x g x h =(1/2) kx2

EACH TIME YOU CALCULATE ONE THE ANSWER FOR THE OTHERS IS THE SAME FOR ONE SYSTEM.

A 600 kg roller coaster car is lifted to the top A 600 kg roller coaster car is lifted to the top of the first hill, of the first hill, 55 m55 m above the ground. above the ground. How much Potential Energy is this?

Use mass x gravity x height

GPE = 600 x 9.8 x 55 GPE = 323400 JHow much Kinetic Energy does it have as it falls? 323400 J. How much work did it take to lift it?323400 J. The answer is always the same.

Example:

Energy is Energy is Energy

• No matter which one you are asked to calculate the other energies will have the same answer in a system.

• This means only calculate the answer one time and use the answer for all four energies.

• Carefully read over the next slide. This will illustrate the point about always using the same answer for calculating energies.

• Remember: Energy cannot be created or destroyed, it can only change form.

Gravitational Potential Energy energy due to positionPE = mgh

Ex. You lift a 1.2 kg book from the first floor to your social studies class on the 2nd floor 5 m up. How much potential energy does the book have?

PE= m g h = (1.2) (9.8) (5) = 58.8 J

How much work did you do? Conservation!!!

W = PE = 58.8 J

Kinetic Energy energy due to motion

KE = ½ mv2

Ex. How much KE does an 1800 kg car going 25 mph (11.2 m/s) have?

KE = ½ mv2

= ½(1800)(11.2)2

= 113 000 J

How much work would friction need to do to stop it?

W = KE = -113 000 JIt’s the same answer because of conservation.

The answer is the same because of conservation of

energy.

Sample ProblemA disgruntled physics student drops her 1.7 kg book off a 4 story building (12 m), What is the potential energy?

What is the Kinetic Energy? What was the work done to lift it?

h = 12 mm = 1.7 kg

PE = m x g x h

PE = 1.7 x 9.8 x 12

PE = 199.92 J

KE = 199.92 J and W = 199.92 J

!

Describe the energy transfer in the following Different Scenarios

• Dropping an object off a building

• Throwing an object off a building

• Car being slowed down by friction

• You throwing a ball

• A bullet shot; then embedded in a tree

• You lifting your backpack up to math

Work Energy Theorem

W = Change in KEW = Change in PE

W = Change in SPE

In order to change any type of energy,

work must be done.

Work Energy Theorem practice

• A 2.5 kg apple hangs from a tree 5 meters up. It falls to the ground. What is the potential energy of the apple in the tree?

• What is the final velocity of the apple just before it hits the ground?

• PE = m x g x h• 2.5 x 9.8 x 5 Ans. 122.5 J• KE = ½ mv2 • 122.5 J = ½ x 2.5 x v2 122.5 = 1.25 x v2 • 122.5/1.25 = v2

• 98 = v2 So take the square root to get v 9.9 m/s = v

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