Slide / 22 Slide 2 / 22 8th Grade Energy of Objects of Motion 205-0-28 www.njctl.org Slide 3 / 22 Energy of Objects in Motion Slide 4 / 22 Review from Last Unit Energy and its Forms Mechanical Energy Energy of Motion Stored Energy Conservation of Energy Types of Energy Resources Click on the topic to go to that section In the previous units we have been studying the motion of objects. We talked about how far and fast an object goes if a force is applied to it. Why does a force cause an object to accelerate? Slide 4 () / 22 Slide 5 / 22 Review from Last Unit In the previous units we have been studying the motion of objects. We talked about how By far applying and fast a force an object onto an goes object, if a energy force is applied is given to the to object. it. This energy is added to the amount of energy the object Why does already a force possessed. cause an object to accelerate? If a resistive force is applied onto an object, then the force is taking energy away from the object causing it to decelerate. Energy and its Forms Return to Table of Contents
Slide 6 / 22 What is Energy? Slide 7 / 22 What is Energy? Energy is a measurement of an object's ability to do work. How would you define work? How would you know if any work was being done? Energy is a measurement of an object's ability to do work. Work is defined as applying a force in order to move an object in a given direction. When work is done on an object by another object, there is a transfer of energy between objects. Since energy is equal to work, the unit for both is the same, the Joule (J). Joule = Newton-meter Slide 8 / 22 Work Work can only be done to a system by an external force; a force from something that is not a part of the system. Slide 9 / 22 Work The amount of work done is the change in the amount of energy that the system will experience. This is given by the equation: So let's say our system is a plane. The gate assistance vehicle is not part of the system. When the vehicle comes along and pushes back the plane, it increases the energy of the plane. The assistance truck is an outside force doing work on the plane. Slide 0 / 22 Positive Work W = E final - E initial Fill in the blanks with "positive" or "negative". HINT: Think about how these statements relate to acceleration. When a force is applied to an object that causes it to speed up and move a distance, the work is. When a resistive force is applied to an object that causes it to slow down over a distance, or not move at all, the work would be. Slide / 22 Negative Work If an object moves in the same direction as the direction of the force applied to it, the energy of the system is increased. The work is positive: W > 0. If an object moves in the direction opposite to the direction of the force applied to it, then the work is negative: W < 0. The energy of the system is reduced. The parachute moves downwards, while air resistance acts upwards on the parachute. They can push the truck to get it to move!
If an object does not move even when there is a force applied to it, then no work is done on the object! W=0 J Slide 2 / 22 Zero Work The people exert a force onto the wall, but the wall does not move! Mechanical Energy - The energy of an object due to its motion and position. Mechanical energy is usually used to describe a large object. It is the sum of kinetic and potential energy. Slide 3 / 22 Mechanical vs. Non-Mechanical Energy Energy exists in many forms, but can be broken down into two major forms: Non-Mechanical Energy The energy of an object that is not due to its motion or position. Nonmechanical energy usually describes an object at its atomic level. Examples: electrical energy chemical energy thermal energy sound energy Slide 4 / 22 Which of the following is the unit for energy? Slide 4 () / 22 Which of the following is the unit for energy? A Meter A Meter B Newton B Newton C Second D Joule C Second D Joule D Slide 5 / 22 2 A wagon is rolling down a hill. A man tries to stop the wagon by trying to push it back up the hill, but he is unsuccessful. Is the man doing positive or negative work? Slide 5 () / 22 2 A wagon is rolling down a hill. A man tries to stop the wagon by trying to push it back up the hill, but he is unsuccessful. Is the man doing positive or negative work? A positive B negative A positive B negative B
Slide 6 / 22 3 A boy kicks a soccer ball into a net. Did the boy do positive or negative work on the ball? Slide 6 () / 22 3 A boy kicks a soccer ball into a net. Did the boy do positive or negative work on the ball? A positive A positive B negative B negative A Slide 7 / 22 Slide 7 () / 22 4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery. Is the salt doing positive or negative work on the woman's shoes? 4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery. Is the salt doing positive or negative work on the woman's shoes? A positive B negative A positive B negative B Slide 8 / 22 Slide 8 () / 22 5 Jill is waiting for the bus and she forgot her mittens. She rubs her hands together to keep them warm. In this situation, there is energy due to the movement of her hands. There is also energy due to the heat she generates by rubbing her hands together. 5 Jill is waiting for the bus and she forgot her mittens. She rubs her hands together to keep them warm. In this situation, there is energy due to the movement of her hands. There is also energy due to the heat she generates by rubbing her hands together. A mechanical, non-mechanical B non-mechanical, mechanical A mechanical, non-mechanical A B non-mechanical, mechanical
Slide 9 / 22 Mechanical Energy Slide 20 / 22 Forms of Mechanical Energy Mechanical Energy can be broken down into two different types of Energy: energy of motion, which is called Kinetic Energy and stored energy, which is called Potential Energy. Potential Energy has two forms, Gravitational and Elastic, depending upon how the energy is stored. Energy Write the underlined words into the correct place in the diagram. Energy Energy Return to Table of Contents Slide 2 / 22 6 Which of the following is a form of mechanical energy? Slide 2 () / 22 6 Which of the following is a form of mechanical energy? A Kinetic A Kinetic B Thermal C Chemical B Thermal C Chemical A - Kinetic D Solar D Solar Slide 22 / 22 Slide 23 / 22 7 Which of the following is a type of energy which is used to describe the motion of an object? A Electrical Energy Energy of Motion B Nuclear Energy C Kinetic Energy D All of the above Return to Table of Contents
Slide 23 () / 22 7 Which of the following is a type of energy which is used to describe the motion of an object? Slide 24 / 22 Energy of Motion A Electrical Energy In order for an object to move, one of two scenarios has to occur: B Nuclear Energy C Kinetic Energy C - Kinetic. The object uses some of the potential energy that it had stored. 2. Energy is transferred to the object from an outside source. D All of the above In either case, now that the object is in motion, the object is experiencing kinetic energy. Slide 25 / 22 Kinetic Energy An object's state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time. Slide 26 / 22 Kinetic Energy The amount of kinetic energy that an object possesses is dependent on two factors: mass and velocity Since the state of motion of an object can change with time, the kinetic energy of an object can also change with time. Both of these factors are directly proportional to the kinetic energy. We talked about this mathematical relationship in the last chapter. What did directly proportional mean? Slide 27 / 22 Kinetic Energy, Mass, Velocity The larger the mass, the more energy is needed to move the object, Slide 28 / 22 How Does Kinetic Energy Depend on Mass? If two identical objects are moving at the same velocity, they will have the same kinetic energy. therefore the the kinetic energy. However, if one object has more mass than the other, the heavier object will have more kinetic energy. v = 5 m/s v = 5 m/s Since kinetic energy is the energy of motion, the object has to have a velocity to have kinetic energy. The larger the velocity, the the kinetic energy. A tennis ball and a bowling ball are both shown above. The bowling ball is heavier than the tennis ball. Which ball would have more kinetic energy?
Slide 29 / 22 Velocity vs. Speed Remember that velocity is another way to measure motion. V elocity is the speed of an object with direction. Speed does not have a direction, so we call speed a scalar quantity. Since velocity has both magnitude and direction, it is a vector quantity. Slide 30 / 22 How Does Kinetic Energy Depend on Velocity? In this picture, the hare is moving faster than the tortoise at this point. Runner's speed: 0 km/hr Runner's velocity: 0 km/hr to the East If we assumed that they had the same mass, who would have more kinetic energy? Why? Discuss this with a partner. Slide 3 / 22 How Does Kinetic Energy Depend upon Velocity? If two identical objects are moving at the same velocity then they will have the same kinetic energy. However, if one of the objects is moving faster, the faster one will have more kinetic energy. Slide 32 / 22 8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 m/s. Which of the following cars have the most kinetic energy at that moment? A a police car v = 5 m/s v = 0 m/s B an ambulance In the diagram above, two identical tennis balls are moving. Which tennis ball has more kinetic energy and why? C a firetruck D they all have the same kinetic energy Slide 32 () / 22 8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 m/s. Which of the following cars have the most kinetic energy at that moment? Slide 33 / 22 9 Three different baseball pitchers had the speed of their fastball measured by a radar gun. Which of the following pitcher's fastball had the smallest amount of kinetic energy? A a police car A a little league pitcher (22 m/s) B an ambulance C B a high school pitcher (33 m/s) C a major league pitcher (4m/s) C a firetruck D they all had the same kinetic energy D they all have the same kinetic energy
Slide 33 () / 22 9 Three different baseball pitchers had the speed of their fastball measured by a radar gun. Which of the following pitcher's fastball had the smallest amount of kinetic energy? Slide 34 / 22 0 Which of the following situations has the least kinetic energy? Be ready to explain your answer. A a man sitting still on a park bench A a little league pitcher (22 m/s) B a high school pitcher (33 m/s) C a major league pitcher (4m/s) D they all had the same kinetic energy A B a child riding a bike C a woman driving a car D it is impossible to tell Slide 34 () / 22 0 Which of the following situations has the least kinetic energy? Be ready to explain your answer. Slide 35 / 22 Calculating Kinetic Energy Kinetic energy can be solved for by using the equation: A a man sitting still on a park bench B a child riding a bike C a woman driving a car D it is impossible to tell A Name Kinetic Energy KE = 2 mv 2 Let's fill in the table below. variable m units m/s Slide 36 / 22 Example - Calculating Kinetic Energy A car, which has a mass of,000 kg, is moving with a velocity of 5 m/s. How much kinetic energy does the car possess? Calculate the car's kinetic energy. KE = 2 mv 2 KE = (0.5)(000 kg)(5 m/s) 2 KE = (0.5)(000 kg)(25 m 2 /s 2 ) KE = 25,000 J Slide 36 () / 22 Example - Calculating Kinetic Energy A car, which has a mass of,000 kg, is moving with a velocity of 5 m/s. How much kinetic energy does the car possess? Calculate the car's kinetic energy. Please note that there are multiple ways to model the math of this problem. We suggest showing your students at least two ways and then continuing KE to = use 2 mv 2 the model that a KE majority = (0.5)(000 of your kg)(5 students m/s) prefer. 2 Teacher Notes KE = (0.5)(000 kg)(25 m 2 /s 2 ) KE = 25,000 J Click on the box to see the solution. [This object is a teacher notes pull Click on the box to see the solution.
Slide 37 / 22 A 0 kg snowball is rolling down a hill. Just before reaching the bottom, its velocity is measured to be 0 m/s. What is the kinetic energy of the ball at this position? Slide 37 () / 22 A 0 kg snowball is rolling down a hill. Just before reaching the bottom, its velocity is measured to be 0 m/s. What is the kinetic energy of the ball at this position? KE= /2 mv 2 KE= /2 (0 kg) (0 m/s) 2 KE= /2 (0 kg) (00m 2 /s 2 ) KE= 500 J Slide 38 / 22 2 A 00 kg running back in football is running with a velocity of 2 m/s. What is his kinetic energy? Slide 38 () / 22 2 A 00 kg running back in football is running with a velocity of 2 m/s. What is his kinetic energy? KE= /2 mv 2 KE= /2 (00 kg) (2 m/s) 2 KE= /2 (00 kg) (4m 2 /s 2 ) KE= 200 J Slide 39 / 22 3 A 2000 kg car with a velocity of 20 m/s slows down and stops at a red light. What is the change in kinetic energy? Slide 39 () / 22 3 A 2000 kg car with a velocity of 20 m/s slows down and stops at a red light. What is the change in kinetic energy? KE= /2 mv 2 KE f = 0 J (stopped) KE i= /2 (2000 kg) (20 m/s) 2 KE i= /2 (2000 kg) (400 m 2 /s 2 ) KE i= 400,00J KE f-ke i= 0J-400,000J = - 400,000J negative because it decreased
Slide 40 / 22 4 A 50 kg girl rode her 2 kg bicycle in a race. She started from rest and peddled with a velocity of 0 m/s. What is the change in kinetic energy of the girl and her bicycle? Slide 40 () / 22 4 A 50 kg girl rode her 2 kg bicycle in a race. She started from rest and peddled with a velocity of 0 m/s. What is the change in kinetic energy of the girl and her bicycle? KE= /2 mv 2 KE i = 0 J (stopped) KE f= /2 (50 kg +2 kg) (0 m/s) 2 KE f= /2 (62 kg) (00 m 2 /s 2 ) KE f= 300 J KE f-ke i= 300J-0J = 300 J positive because it increased Slide 4 / 22 Thinking Mathematically KE = 2 mv 2 We have already said that mass is directly proportional to kinetic energy. Slide 42 / 22 5 If the mass of a wagon is doubled, its kinetic energy: A increases B decreases This means that if the mass of the object doubles, the kinetic energy. doubles If the mass of the object increases by a factor of 5, then the kinetic energy increases by. a factor of 5 If the mass of the object decreases by half, then the kinetic energy will decrease by. half Slide 42 () / 22 5 If the mass of a wagon is doubled, its kinetic energy: A increases Slide 43 / 22 6 If the mass of a wagon is doubled, by what factor does the kinetic energy increase? B decreases A
Slide 43 () / 22 6 If the mass of a wagon is doubled, by what factor does the kinetic energy increase? Slide 44 / 22 Thinking Mathematically Kinetic energy can be solved by using the equation: KE = mv 2 2 2 From the equation, we can see that the kinetic energy is also directly proportional to the square of the velocity. This means that if the velocity doubles, the kinetic energy increases by a factor of 4. 2 2 =4 Slide 45 / 22 If the velocity is quadrupled, then the kinetic energy increases by a factor of 6. 4 2 = 6 Slide 45 () / 22 7 If the velocity of a wagon is tripled, its kinetic energy: 7 If the velocity of a wagon is tripled, its kinetic energy: A increases B decreases A increases B decreases A Slide 46 / 22 8 If the velocity of a wagon is tripled, by what factor does the kinetic energy increase? Slide 46 () / 22 8 If the velocity of a wagon is tripled, by what factor does the kinetic energy increase? 9
Slide 47 / 22 9 Two balls are moving with the same velocity, ball A has a mass of 0 kg and ball B has a mass of 40 kg. How much more kinetic energy does ball B have? Slide 47 () / 22 9 Two balls are moving with the same velocity, ball A has a mass of 0 kg and ball B has a mass of 40 kg. How much more kinetic energy does ball B have? 4 times Slide 48 / 22 20 A cart halves its mass and at the same time doubles its speed. Does the kinetic energy increase or decrease? By what factor does the kinetic energy change? Slide 48 () / 22 20 A cart halves its mass and at the same time doubles its speed. Does the kinetic energy increase or decrease? By what factor does the kinetic energy change? A increase, 2 B increase, 4 C decrease, 2 A increase, 2 B increase, half the 4mass gives /2 the KE, double the speed gives 4 x KE therefore (/2)(4)= 2 C decrease, 2 D decrease, 4 D decrease, 4 A Slide 49 / 22 Slide 50 / 22 Where does Kinetic Energy Come From? Imagine a roller coaster car that is at the top of the first hill and is stopped. Stored Energy Does the car stay stopped at the top of the hill for the entire ride? What happens? Return to Table of Contents
Slide 5 / 22 Where does Kinetic Energy Come From? Slide 52 / 22 Where does Kinetic Energy Come From? Once the car leans over the edge, gravity pulls it down. The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls. The kinetic energy the car is receiving is coming from another type of energy called potential energy. Potential energy is energy stored in an object due to the object's position. The roller coaster car on the previous slide had stored energy due to its height above the ground. There are two forms of potential energy that we will be looking at in this unit: Gravitational Potential Energy and Elastic Potential Energy Slide 53 / 22 Gravitational Potential Energy Slide 54 / 22 Gravitational Potential Energy The potential energy due to elevated positions is called gravitational potential energy. Gravitational potential energy is stored energy and it can be used at a later time to cause an object to move. Once the person steps off the diving board, the gravitational potential energy is converted into kinetic energy and the person falls (moves!) Slide 55 / 22 Gravitational Potential Energy Gravitational potential energy is determined by three factors: mass, gravitational acceleration, and height. All three factors are directly proportional to energy. Work is required to elevate objects against Earth's gravity. For example, work is done on the truck to elevate it off the ground. The amount of work done on the truck is equal to the truck's gravitational potential energy at this new height. Slide 56 / 22 How Does Mass Affect Gravitational Potential Energy? In this picture, the mass of a tennis ball was doubled when it was at the same height off of the ground. Mass: The heavier the object is, the more gravitational potential energy the object has. Gravitational Acceleration: The larger the 'g', the more gravitational potential energy the object has. Since gravity on Earth is considered a constant, this will not change. m = 2 kg m = kg h = 2 m h = 2 m How does the gravitational potential energy compare for the two objects? Height: The higher the object is off the ground, the more gravitational potential energy the object has.
Slide 57 / 22 How Does Mass Affect Gravitational Potential Energy? Slide 58 / 22 How Does Height Affect Gravitational Potential Energy? In this picture, a tennis ball is lifted to a height that is twice as high. m = 2 kg m = kg Mass: doubled h = 2 m h = 2 m Gravitational Acceleration: stayed the same, no change Height: stayed the same, no change h = 4 m How would the gravitational potential energy compare at the higher height? h = 2 m Since the only thing that changed was the mass, which doubled, the gravitational potential energy also doubled. Slide 59 / 22 How Does Height Affect Gravitational Potential Energy? Slide 60 / 22 2 A bowling ball, which has a mass that is 30 times larger than a softball, is lifted to the same height as the softball. How does the gravitational potential energy of the bowling ball compare to the softball? h = 4 m h = 2 m Mass: stayed the same, no change Gravitational Acceleration: stayed the same, no change Height: doubled A they are the same B thirty times smaller C ten times as large D thirty times as large Since the only thing that changed was the height which doubled, the gravitational potential energy also doubled. Slide 60 () / 22 2 A bowling ball, which has a mass that is 30 times larger than a softball, is lifted to the same height as the softball. How does the gravitational potential energy of the bowling ball compare to the softball? A they are the same Slide 6 / 22 22 Two balloons are floating in the sky. If one balloon is floating at a height of 30 m and the other identical balloon, is floating at a height of 45 m, how much larger is the gravitational potential energy of the higher balloon compared to the lower one? A half as large B thirty times smaller C ten times as large D thirty times as large D B they are the same C.5 times larger D twice as large
Slide 6 () / 22 22 Two balloons are floating in the sky. If one balloon is floating at a height of 30 m and the other identical balloon, is floating at a height of 45 m, how much larger is the gravitational potential energy of the higher balloon compared to the lower one? A half as large B they are the same C.5 times larger D twice as large C Slide 62 / 22 Calculating Gravitational Potential Energy Gravitational potential energy can be solved by using the equation: Name Gravitational Potential Energy Gravity GPE = mgh Let's fill in the table below. variable m units m Slide 63 / 22 Example - Calculating Gravitational Potential Energy Slide 64 / 22 23 A 50 kg diver is standing on top of a 0 m platform. How much gravitational potential energy does he have? A basketball with a mass of 0.5 kg, is held at a height of 2 m above the ground. How much gravitational potential energy does the basketball possess? GPE = mgh GPE = (0.5 kg)(9.8 m/s 2 )(2 m) GPE = 9.8 J Click on the box to see the solution. Slide 64 () / 22 23 A 50 kg diver is standing on top of a 0 m platform. How much gravitational potential energy does he have? Slide 65 / 22 24 A 3,000 kg hot air balloon is hovering at a height of 00 m above Earth's surface. How much gravitational potential energy does it possess? GPE= mgh = 50 kg(9.8 m/s 2 )(0 m) = 4,900 J
Slide 65 () / 22 24 A 3,000 kg hot air balloon is hovering at a height of 00 m above Earth's surface. How much gravitational potential energy does it possess? GPE= mgh = 3000 kg(9.8 m/s 2 )(00 m) = 294,000,000 J Slide 66 / 22 Thinking Mathematically GPE = mgh GPE = mgh GPE = mgh We know that GPE is directly proportional to mass, to gravity, and to height. This means that as any of these increase, the GPE increases by the same factor. If any of these decrease, then the GPE decreases by the same factor. GPE = mgh GPE = mgh GPE = mgh Slide 67 / 22 25 A ball is at a height of 30 m. It is then moved to a height of 60m. By what factor does the GPE increase? Slide 67 () / 22 25 A ball is at a height of 30 m. It is then moved to a height of 60m. By what factor does the GPE increase? 2 Slide 68 / 22 26 A 3 kg object and a 9 kg object are elevated from the same height. Which has more GPE? A 3 kg object Slide 68 () / 22 26 A 3 kg object and a 9 kg object are elevated from the same height. Which has more GPE? A 3 kg object B 9 kg object B 9 kg object B
Slide 69 / 22 27 A 3 kg object and a 9 kg object are dropped from the same height. How much less is the GPE of the 3 kg object than the 9 kg object? Slide 69 () / 22 27 A 3 kg object and a 9 kg object are dropped from the same height. How much less is the GPE of the 3 kg object than the 9 kg object? /3 Slide 70 / 22 28 An object is 5 m above the ground. The object triples its mass and doubles its height. By what factor does the object's GPE change? Slide 70 () / 22 28 An object is 5 m above the ground. The object triples its mass and doubles its height. By what factor does the object's GPE change? 6 Slide 7 / 22 Elastic Potential Energy Another type of stored energy is called elastic potential energy. Looking at the picture to the right, can you come up with an idea about what elastic potential energy is? Slide 72 / 22 Elastic Potential Energy Elastic potential energy is determined by two factors: the elasticity of the material and how far it is stretched or compressed. Think about what you know about rubber bands. Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy? Talk about this at your table.
Slide 73 / 22 Elastic Potential Energy Slide 74 / 22 What is the Difference Between Stretching and Compression in a Spring? Elasticity: The more elastic a material is, the more elastic potential energy the object has. Distance of stretch (or compression): The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has. Think about a slinky sitting on a desk. A spring has no potential energy stored in it if it is neither stretched nor compressed. This relaxed state is shown in figure (a). Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length, as shown in figure (b). (a) (b) (c) Slide 75 / 22 What is the Difference Between Stretching and Compression in a Spring? Compressing a spring is caused when the spring is squeezed. This causes a decrease in the length of the spring compared to the relaxed length, as shown in figure (c). The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance, x. relaxed stretched compressed Slide 76 / 22 How Does Elastic Potential Energy Depend Upon Compression and Stretching? Both pictures to the right show a spring, which is an elastic material. In the top picture the spring is stretched from its relaxed state. In the bottom picture, the spring is compressed from its relaxed state. no EPE stored (a) (b) (c) For each case, is elastic potential energy stored in the spring? Slide 77 / 22 Slide 77 () / 22 29 A child jumps on a trampoline. When will the trampoline have more elastic potential energy? A When the child is standing on the trampoline B When the child is in the air C When the child lands on the trampoline after jumping D The trampoline will always have the same elastic potential energy 29 A child jumps on a trampoline. When will the trampoline have more elastic potential energy? A When the child is standing on the trampoline B When the child is in the air C When the child lands on the trampoline after C jumping D The trampoline will always have the same elastic potential energy
Slide 78 / 22 Calculating Elastic Potential Energy Elastic potential energy can be solved by using the equation: EPE = kx 2 2 EPE = Elastic Potential Energy (J) k = spring constant (N/m) x = distance of stretch or compression (m) Slide 79 / 22 Spring Constant EPE = 2 kx 2 The energy and distance variables in this equation are likely familiar. But what is the spring constant (k)? Look at the two springs to the right. Which do you think would be easier to stretch? Every spring has a different degree of stretchiness and that is what the spring constant represents. Breaking down the units for spring constant also explains what the variable represents. Can you explain what Newtons per Meter (N/m) means? Slide 80 / 22 Spring Constant EPE = 2 kx 2 Slide 8 / 22 Example - Calculating Elastic Potential Energy A spring that has a spring constant of 0 N/m, is stretched a distance of m from its relaxed length. How much elastic potential energy is stored in the spring? EPE = 2 kx 2 EPE = ( 2 )(0 N/m)( m) 2 EPE = ( 2 )(0 N/m)( m 2 ) EPE = (5 N*m) EPE = 5 J Click on the box to see the solution. Slide 8 () / 22 Example - Calculating Elastic Potential Energy A spring that has a spring constant of 0 N/m, is stretched a distance of m from Please its relaxed note that length. there How are much multiple elastic potential energy is stored ways to in model the spring? the math of this problem. We suggest showing your students at least two ways and then continuing to use the model that a majority EPE of your = 2 students kx 2 prefer. EPE = ( 2 )(0 N/m)( m) 2 EPE = ( 2 )(0 N/m)( m 2 ) EPE = (5 N*m) Teacher Notes EPE = 5 J [This object is a teacher notes pull Slide 82 / 22 30 A child bouncing on a pogo stick compresses the spring by 0.25 m. If the spring constant of the spring on the bottom of the pogo stick is 200 N/m, what is the elastic potential energy stored in the spring when it is compressed? Click on the box to see the solution.
Slide 82 () / 22 30 A child bouncing on a pogo stick compresses the spring by 0.25 m. If the spring constant of the spring on the bottom of the pogo stick is 200 N/m, what is the elastic potential energy stored in the spring when it is compressed? Slide 83 / 22 3 A rubber band with a spring constant of 40 N/m is pulled back 0.5 m. How much elastic potential energy is stored in the elastic band? EPE= /2 kx 2 = /2 (200 N/m) (0.25 m) 2 = /2 (200 N/m)(0.0625 m 2 ) = 00 N/m (0.0625 m 2 ) EPE = 6.25 J Slide 83 () / 22 3 A rubber band with a spring constant of 40 N/m is pulled back 0.5 m. How much elastic potential energy is stored in the elastic band? Slide 84 / 22 32 Which of the following would you expect to have the smallest spring constant? A a garage door spring EPE= /2 kx 2 = /2 (40 N/m) (0.5 m) 2 = 20 N/m (0.25 m 2 ) EPE = 5 J B a slinky C a spring in a pen D a trampoline spring Slide 84 () / 22 32 Which of the following would you expect to have the smallest spring constant? A a garage door spring B a slinky C a spring in a pen D a trampoline spring C Slide 85 / 22 Thinking Mathematically EPE = kx 2 2 KE = mv 2 2 Notice that the equation for EPE is similar to the equation for KE. Remember that in the equation for KE, energy was directly proportional to the mass and it was also directly proportional to the square of the velocity. What do you think the relationship is between EPE and the spring constant, k? What do you think is the relationship between EPE and the distance, x, the spring is stretched or compressed?
Slide 86 / 22 Thinking Mathematically EPE = 2 kx 2 Slide 87 / 22 33 If the spring constant, k, is tripled, by what factor does the EPE increase? EPE is directly proportional to the spring constant. EPE is directly proportional to the square of the distance the spring is compressed or stretched. Slide 87 () / 22 33 If the spring constant, k, is tripled, by what factor does the EPE increase? Slide 88 / 22 34 If the spring constant, k, is halved, by what factor does the EPE decrease? 3 Slide 88 () / 22 34 If the spring constant, k, is halved, by what factor does the EPE decrease? Slide 89 / 22 35 If the distance a spring is stretched is increased by a factor of 6, by what factor is the EPE increased? /2
Slide 89 () / 22 Slide 90 / 22 35 If the distance a spring is stretched is increased by a factor of 6, by what factor is the EPE increased? 36 Conservation of Energy Return to Table of Contents Slide 9 / 22 Slide 92 / 22 Conservation of Energy What we have looked at so far is that an object has kinetic energy if the object is in motion. The faster that the object is going, the more kinetic energy it has. In order for an object's kinetic energy to increase, it must get energy from somewhere. But where would it get that energy? Conservation of Energy In order for an object's kinetic energy to increase, it must take energy from its stored energy, which we call potential energy. When this happens, the potential energy that an object possesses decreases. Even though kinetic and potential energy are changing, the Total Energy (TE) in that closed system contains does not change. Hint: think back to the roller coaster. What kind of energy did it have at the top of the hill? This is called the Conservation of Energy. initial Total Energy = final Total Energy TE i = TE f Slide 93 / 22 Conservation of Energy When energy is conserved, no energy is added or taken away from the system. The total energy you start with is the total energy you end with. TE i = TE f In other words, energy can not be created or destroyed. It can only be transformed from one form to another. Click here to see conservation of energy explained in roller coasters! Slide 94 / 22 When looking at the mechanical energy of a system, the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together. Therefore, another way to write conservation of energy is like this: When would PE be zero? the object is on the ground (GPE) when a spring or other elastic material is not stretched or compressed (EPE) Conservation of Energy (PE + KE) i = (PE + KE) f When would KE be zero? the object is not moving
Slide 95 / 22 Conservation of Energy Let's see if we can determine the total energy of a ball that is dropped from rest. The figure below shows the ball at different positions as it falls, starting with when it's at rest at m before being dropped. Use the idea of conservation of energy to determine the missing values. v= 0 m/s Height = m Remember that the total mechanical energy at that position is the sum of the two individual energies: (PE + KE) Slide 96 / 22 At position A in the diagram below, the roller coaster car has 40 J of total energy and has a velocity equal to 0 m/s. How much kinetic energy does the car possess at Point A? 0 J How much gravitational potential energy does the car possess at Point A? 40 J TE = 0.5 J PE = 0.5 J KE = 0 J Height = 0.5 m TE = 0.5 J PE = 0.25 J KE = 0.25 J Height = 0 m TE = 0.5 J PE = 0 J KE = 0.5 J 40 J 5 J 25 J Slide 97 / 22 At position B in the diagram below, the roller coaster car has a gravitational potential energy equal to 5 J. Slide 98 / 22 At position C in the diagram below, the roller coaster car has a gravitational potential energy equal to 25 J. How much total energy does the car possess at Point B? 40 J How much kinetic energy does the car possess at Point B? 25 J How much total energy does the car possess at Point C? 40 J How much kinetic energy does the car possess at Point C? 5 J 40 J 5 J 25 J 40 J 5 J 25 J Slide 99 / 22 36 At what position in the diagram below does the object have only gravitational potential energy? Slide 99 () / 22 36 At what position in the diagram below does the object have only gravitational potential energy? A W A W B C X Y B C X Y A D E Z None of the above D E Z None of the above h = 0 m h = 0 m
Slide 00 / 22 37 At what position in the diagram below does the object have only kinetic energy? Slide 00 () / 22 37 At what position in the diagram below does the object have only kinetic energy? A W A W B C X Y B C X Y B D E Z None of the above D E Z None of the above h = 0 m h = 0 m Slide 0 / 22 38 At what position in the diagram below does the object have both gravitational potential and kinetic energy? Choose all that apply. A W Slide 0 () / 22 38 At what position in the diagram below does the object have both gravitational potential and kinetic energy? Choose all that apply. A W B X B X C and D C Y C Y D Z D Z E None of the above h = 0 m E None of the above h = 0 m Slide 02 / 22 Transfer of Kinetic Energy to Potential Energy Just as potential energy can be transferred to kinetic energy, kinetic energy can be transferred into potential energy. v= 0 m/s Height = m TE = 0.5 J PE = 0.5 J KE = 0 J The total energy of the object must always be the same due to conservation of energy. Let's look at the ball that is dropped from m again. Suppose the ball bounces after it hits the ground. What will happen to the KE? Height = 0.5 m TE = 0.5 J PE = 0.25 J KE = 0.25 J Height = 0 m TE = 0.5 J PE = 0 J KE = 0.5 J Slide 03 / 22 Transfer of Kinetic Energy to Potential Energy The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height. Because of conservation of energy, the total energy stays the same! Height = 0 m TE = 0.5 J PE = 0 J KE = 0.5 J Height = 0.5 m TE = 0.5 J PE = 0.25 J KE = 0.25 J v= 0 m/s Height = m TE = 0.5 J PE = 0.5 J KE = 0 J
Slide 04 / 22 Transfer of Kinetic Energy to Potential Energy In reality, the ball will not bounce as high as it was dropped. Does this mean energy was lost? No. It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka Non-Mechanical Energy). If we consider the ball and the ground to be a closed system, then the system's total energy stays the same! TE = 0.5 J PE = 0 J KE = 0.5 J TE = 0.5 J PE = 0.25 J KE = 0.5 J TE = 0.5 J PE = 0.4 J KE = 0 J v= 0 m/s Height < m Slide 05 / 22 Transfer of Kinetic Energy to Potential Energy Kinetic energy can also be transferred to elastic potential energy. Conservation of energy of still applies, which means the total energy remains constant. Let's consider a system that is composed of a block and a spring as shown to the right. Sound Energy! NME = 0.0 J NME=0.0 J Slide 06 / 22 Transfer of Kinetic Energy to Elastic Potential Energy Slide 07 / 22 39 In which position of the block would the system have only EPE? In the top picture, the block is travelling at 0 m/s, meaning that it has kinetic energy. The spring is relaxed and therefore has no elastic potential energy. The total energy of the blockspring system is entirely due to the KE of the block right now. A B C In the bottom picture, the block has compressed the spring and is no longer moving. The block has transferred its kinetic energy to elastic potential energy in the spring. The total energy of the block-spring system is entirely due to the elastic potential energy in the spring. Slide 07 () / 22 39 In which position of the block would the system have only EPE? Slide 08 / 22 40 In which position of the block would the system have both KE and EPE? A B C C A B C
Slide 08 () / 22 40 In which position of the block would the system have both KE and EPE? Slide 09 / 22 4 In which position of the block would the system have only KE? A B C B A B C Slide 09 () / 22 4 In which position of the block would the system have only KE? A B C A Slide 0 / 22 What if the Total Energy is not equal at the beginning and the end? If the total amount of energy that we start with, E i, does not equal the total amount of energy that we end up with, "E f", then energy was not conserved TE i TE f This means that there was an outside force that acted on the system. Let's look at the dropping ball again. Last time we considered the ball and the ground as the system together. What if we just considered the ball as the system by itself? TE = 0.5 J TE = 0.5 J PE = 0 J KE = 0.5 J Slide / 22 What if the Total Energy is not equal at the beginning and the end? The total energy of the ball before the bounce and after the bounce would be different. This is because the ground would now be an outside force acting on the system, the ball. TE = 0.4 J PE = 0.25 J KE = 0.5 J TE = 0.4 J PE = 0.4 J KE = 0 J v= 0 m/s Height < m Slide 2 / 22 Types of Energy Resources Sound Energy! NME = 0.0 J NME=0.0 J Return to Table of Contents
Slide 3 / 22 Energy Resources Slide 4 / 22 Types of Energy Resources Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources. Energy resources can be broken down into two categories: Renewable and Non-Renewable. Renewable Energy Resources are natural resources that can replenish themselves over time. Non-Renewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner. Slide 5 / 22 Energy Production from the Sun Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun. When the photons hit the solar panels, charged particles are free to move which causes a current to be produced. This current is converted to usable electricity by the home. Solar energy is converted to electrical energy! Slide 7 / 22 Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam. Gravitational potential energy is stored in elevated water. When the water is released downward towards a turbine, the GPE is converted to kinetic energy and spins the turbine. The turbine is connected to a generator that converts this mechanical energy to electrical energy! Slide 6 / 22 Energy Production from the Wind Wind is a renewable energy resource that is used to create electricity by wind turbines, such as in the Alta Wind Energy Center in California, the world's largest wind farm. As the wind blows past the blades of the turbine, the kinetic energy of the wind is transferred to the blades. Inside the column of the turbine, there is a drive shaft which is connected to a generator. As the blades spin, it spins the drive shaft that is connected to a generator. The generator converts the kinetic energy (mechanical energy) into electrical energy! Slide 8 / 22 Energy Production from Fossil Fuels Fossil fuels are a non-renewable energy resource that can be used to produce electricity when it is burned. Fossil fuels include: natural gas, oil, and coal (shown to the right). When the fuel is burned, the heat turns water into steam which turn the blades of a turbine (kinetic energy!). The turbine is connected to a generator that converts the mechanical energy into electrical energy!
Slide 9 / 22 Effects of Using Fossil Fuels As An Energy Resource Fossil fuels are non-renewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy. Fossil fuels take millions of years to be produced. Fossil fuels are also not considered "Clean" energy resources as they produce Carbon Dioxide (CO 2) when burned. Carbon dioxide is considered a greenhouse gas, which many believe is a cause global warming. Slide 20 / 22 42 Which of the following is not considered a renewable energy resource? A Solar B Wind C Hydroelectric (water) D Fossil Fuels Slide 20 () / 22 42 Which of the following is not considered a renewable energy resource? Slide 2 / 22 43 The production of energy by wind, water, the sun, and fossil fuels relies on the principle of conservation of energy. A Solar B Wind C Hydroelectric (water) D True False D Fossil Fuels Slide 2 () / 22 43 The production of energy by wind, water, the sun, and fossil fuels relies on the principle of conservation of energy. Slide 22 / 22 44 The spinning of a generator in wind turbines and hydroelectric dams converts non-mechanical energy into electrical energy. True True False TRUE False
Slide 22 () / 22 44 The spinning of a generator in wind turbines and hydroelectric dams converts non-mechanical energy into electrical energy. True False FALSE they convert mechanical energy into electrical energy