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Hi, I'm Jennifer Pulley, and welcome to NASA Connect, the show that connects you to math,

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science, technology, and NASA.

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Imagine it's the year 2040.

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You and a team of international scientists are part of the exploration crew that will

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begin construction of the first human base on Mars.

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You are laying the groundwork for the next generation of explorers to explore Mars and beyond.

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It's not an easy task, but you are up to the challenge.

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All your years of schooling, training, and hard work have finally paid off.

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Does it sound like a fantasy to you?

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Actually, it's not.

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NASA is ready to make the next step to exploring the solar system and beyond,

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and they need your help.

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NASA is looking for bright, young engineers, scientists, and researchers

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who will make the new vision for space exploration a reality.

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For you, it starts right now, in the classroom.

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Now, during the course of this program, you will be asked to answer several inquiry-based questions.

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After the questions appear on the screen, your teacher will pause the program

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to allow you time to answer and discuss the questions.

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This is your time to explore and become critical thinkers.

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Students working in groups, take a few minutes to answer the following questions.

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1. What comes to mind when you think of work?

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2. How are work and energy related?

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3. What are some forms of energy?

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Briefly describe them and give examples of each.

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It is now time to pause the program and answer the questions.

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So, guys, how did you do with the questions?

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Great job.

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Okay, let's get started.

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So, what is work?

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Well, most people would say they are working when they do anything that requires a physical...

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...or a mental...

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...effort.

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Now, in scientific terms, work is the use of force to move an object a certain distance.

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More specifically, to do work on an object, some part of the force you exert

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must be in the same direction as the object's motion.

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Let's look at the following two examples.

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On the left side, Norbert is lifting a stack of textbooks from the floor.

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And on the right side, he is carrying the stack of textbooks.

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Note the direction of the applied force and motion for each example.

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In which example is Norbert actually doing work?

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If you said the left side, you are correct.

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Why isn't Norbert doing work in the example on the right?

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Well, because no part of the applied force is in the same direction as the object's motion.

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When the force is in the same direction as the motion,

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we can determine the amount of work being done on an object by multiplying force times distance.

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What are the units for work?

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You know that force is measured in newtons, and distance can be measured in meters.

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The product of a force measured in newtons and the distance measured in meters

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is a measurement called a newton meter, or the joule.

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The joule is the standard unit used to measure work.

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One joule of work is done when a force of one newton moves an object one meter.

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Do you have any idea how much a joule of work is?

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I know. Let's take an apple, which weighs about one newton.

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Now, if you lift the apple from the floor to your waist, which is about one meter,

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you do one joule of work on the apple.

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But what happens if I want to lift 100 apples?

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For me, that would take a lot of force, and I don't think I have enough energy to do that.

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Let's go back to our example with the apple.

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Now, I easily have enough energy to lift this apple from the floor to my waist,

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and I know I'm doing work on the apple as I lift it.

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So there must be a relationship between work and energy, right?

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When I lifted the apple from the floor, I caused a change.

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In this case, the change is in the position of the apple.

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An object that has energy has the ability to cause change, or the ability to do work.

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When I worked on the apple, some of my energy was transferred to the apple.

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You can think of work, then, as the transfer of energy.

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As I lifted the apple from the floor to my waist, the apple gained energy.

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You know, guys, energy has many forms, and we'll get to your list in just a few minutes.

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But first, let's focus on two forms of energy, potential energy and kinetic energy.

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Let's take a look at each.

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If I hold the apple still in my hand, does the apple have energy?

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Careful, not all forms of energy involve movement.

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Well, this apple has stored energy.

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We call it potential energy.

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Holding the apple like this gives the apple the potential to fall to the ground.

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Now, if I release the apple, the apple falls.

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The potential energy changes into kinetic energy.

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It is pretty obvious when an object has kinetic energy.

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As long as the object is moving, it's said to have kinetic energy.

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What's more difficult to determine is how much potential energy an object has.

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Let's go back to our example with the apple.

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The potential energy of this apple really depends on height.

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How high or low my hand is from the ground.

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We call this type of potential energy gravitational potential energy.

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Gravitational potential energy depends on mass, gravitational acceleration, and height.

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Near the Earth's surface, gravitational potential energy, or GPE,

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is equal to the product of mass, gravitational acceleration, and height.

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Remember that G is the acceleration caused by Earth's gravity,

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which at sea level equals 9.8 meters per second squared.

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Let me show you an example.

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Suppose a satellite has a mass of 293 kilograms,

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and we lift it to the top of Mount Everest.

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What is the gravitational potential energy of the satellite?

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Well, what do we know?

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We know mass is equal to 293 kilograms.

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Gravitational acceleration is equal to 9.8 meters per second squared.

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And we know the height of Mount Everest, which is approximately 8,850 meters.

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Let's write the equation for gravitational potential energy.

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GPE equals MGH.

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Substituting in our values for mass, acceleration due to gravity, and height,

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we get GPE equals the product of 293 kilograms,

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9.8 meters per second squared, and 8,850 meters.

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The answer turns out to be approximately 25 million.

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Don't forget, I need to assign a unit to that number.

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Units are very important when explaining scientific concepts.

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Do you have any idea what the unit for energy is?

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Let's figure it out.

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The original equation for GPE is MGH.

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Mass times gravity is equal to weight.

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And weight is measured in newtons.

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Remember, weight is a force.

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Therefore, the unit for gravitational potential energy is the newton meter.

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Do you remember from earlier in the program what a newton meter is equivalent to?

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Well, if you said one joule, you're on the ball.

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One newton meter is equivalent to one joule.

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Wait a minute.

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Work is also measured in joules.

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I think we just showed mathematically how energy and work are related to each other.

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Now let's go back to kinetic energy.

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How much kinetic energy do you think an object, say, like a rocket, depends on?

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The kinetic energy of an object depends on both its mass and its velocity.

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The mathematical relationship between kinetic energy, mass, and velocity is

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Notice that the velocity is squared in the equation.

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Remember, guys, the number two is called an exponent.

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The exponent tells you how many times a number or base is used as a factor.

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For example, 2 squared is equal to 2 times 2, which equals 4.

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3 squared is equal to 3 times 3, which equals 9, and so on.

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The term V squared equals V times V.

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So, are you ready to try a problem involving kinetic energy?

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Here's one for you.

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Norbert's Mars rover, with a mass of 210 kilograms, is traveling on the surface of Mars at a speed of 6 meters per second.

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Zot's rover, with a mass of 170 kilograms, is traveling on the surface of Mars at 8 meters per second.

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Predict which rover has more kinetic energy.

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Then verify your prediction mathematically.

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You may now pause the program.

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So, did you make the correct prediction?

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Let's double check your work.

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Solving for the kinetic energy of Norbert's rover, we have

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Kinetic energy is equal to 1 half times 210 kilograms times 6 meters per second quantity squared.

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The kinetic energy of Norbert's rover is equal to 3780 joules.

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Solving for the kinetic energy of Zot's rover, we have

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Kinetic energy is equal to 1 half times 170 kilograms times 8 meters per second quantity squared.

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The kinetic energy of Zot's rover is equal to 5440 joules.

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So, comparing the two values, we see that the kinetic energy for Zot's rover is greater than the kinetic energy for Norbert's rover.

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We now know that an object may possess both kinetic energy and potential energy at the same time.

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Let's go back to our example with the apple.

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Any object that rises and falls experiences a change in its kinetic and potential energy.

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Let's look at this energy transformation as I toss the apple into the air.

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When the apple moves, it possesses kinetic energy.

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As it rises, it slows down.

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Its kinetic energy decreases.

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Because the height increases, its potential energy increases.

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At the highest point, the apple actually stops moving.

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At this point, it no longer has kinetic energy, but it has maximum potential energy.

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As the apple falls, the kinetic energy increases and the potential energy decreases.

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No matter how energy is transformed or transferred, all of the energy is still present somewhere in one form or another.

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This statement is known as the Law of Conservation of Energy.

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As long as you account for all the different forms of energy involved in any process, you will find that the total amount of energy never changes.

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In other words, energy cannot be created or destroyed.

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It just changes form.

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So, do you think you have a pretty good idea of what work and energy, specifically potential and kinetic energy, are all about?

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Well, good, because now it's time to preview this program's hands-on activities.