8th Grade Energy of Objects of Motion 2015-10-28 www.njctl.org - - PDF document
Slide 1 / 122 Slide 2 / 122 8th Grade Energy of Objects of Motion 2015-10-28 www.njctl.org Slide 3 / 122 Energy of Objects in Motion Click on the topic to go to that section Energy and its Forms Mechanical Energy Energy of Motion
2015-10-28 www.njctl.org
· Energy and its Forms
Click on the topic to go to that section
· Mechanical Energy · Types of Energy Resources · Conservation of Energy · Energy of Motion · Stored Energy
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?
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?
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By applying a force onto an object, energy is given to the object. This energy is added to the amount of energy the object already possessed. If a resistive force is applied onto an
away from the object causing it to decelerate.
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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). 1 Joule = 1 Newton-meter
Work can only be done to a system by an external force; a force from something that is not a part of the system.
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.
The amount of work done is the change in the amount of energy that the system will experience. This is given by the equation: W = Efinal - Einitial
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 ____________.
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.
They can push the truck to get it to move!
If an object moves in the direction
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
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
The people exert a force onto the wall, but the wall does not move!
Non-Mechanical Energy The energy of an object that is not due to its motion or position. Non- mechanical energy usually describes an object at its atomic level. Examples: electrical energy chemical energy thermal energy sound energy Mechanical Energy - The energy of an object due to its motion and position. Mechanical energy is usually used to describe a large
It is the sum of kinetic and potential energy.
Energy exists in many forms, but can be broken down into two major forms:
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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. Write the underlined words into the correct place in the diagram.
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In order for an object to move, one of two scenarios has to occur: 1. The object uses some of the potential energy that it had stored. 2. Energy is transferred to the object from an outside source. In either case, now that the object is in motion, the object is experiencing 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.
Since the state of motion
with time, the kinetic energy of an object can also change with time.
velocity mass The amount of kinetic energy that an object possesses is dependent on two factors:
Both of these factors are directly proportional to the kinetic
last chapter. What did directly proportional mean? and
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. The larger the mass, the more energy is needed to move the object, therefore the _______________ the kinetic energy.
If two identical objects are moving at the same velocity, they will have the same kinetic energy.
v = 5 m/s v = 5 m/s
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? However, if one object has more mass than the other, the heavier
energy.
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. Runner's speed: 10 km/hr Runner's velocity: 10 km/hr to the East
In this picture, the hare is moving faster than the tortoise at this point. If we assumed that they had the same mass, who would have more kinetic energy? Why? Discuss this with a partner.
v = 5 m/s v = 10 m/s
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. In the diagram above, two identical tennis balls are moving. Which tennis ball has more kinetic energy and why?
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C
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A
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Kinetic energy can be solved for by using the equation: 1 2
Let's fill in the table below. variable units Name Kinetic Energy
A car, which has a mass of 1,000 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 = mv2 KE = (0.5)(1000 kg)(5 m/s)2 KE = (0.5)(1000 kg)(25 m2/s2) KE = 125,000 J
1 2
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A car, which has a mass of 1,000 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 = mv2 KE = (0.5)(1000 kg)(5 m/s)2 KE = (0.5)(1000 kg)(25 m2/s2) KE = 125,000 J
1 2
Click on the box to see the solution. Teacher Notes
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Please note that there are multiple ways to model the math of this
students at least two ways and then continuing to use the model that a majority of your students prefer.
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KE= 1/2 mv2 KE= 1/2 (10 kg) (10 m/s)2 KE= 1/2 (10 kg) (100m2/s2) KE= 500 J
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KE= 1/2 mv2 KE= 1/2 (100 kg) (2 m/s)2 KE= 1/2 (100 kg) (4m2/s2) KE= 200 J
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Answer KE= 1/2 mv2 KEf = 0 J (stopped) KEi= 1/2 (2000 kg) (20 m/s)2 KEi= 1/2 (2000 kg) (400 m2/s2) KEi= 400,00J KEf-KEi= 0J-400,000J = - 400,000J negative because it decreased
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Answer KE= 1/2 mv2 KEi = 0 J (stopped) KEf= 1/2 (50 kg +12 kg) (10 m/s)2 KEf= 1/2 (62 kg) (100 m2/s2) KEf= 3100 J KEf-KEi= 3100J-0J = 3100 J positive because it increased
KE = mv2 1 2 We have already said that mass is directly proportional to kinetic energy. This means that if the mass of the object doubles, the kinetic energy ___________. If the mass of the object increases by a factor of 5, then the kinetic energy___________ by ______________. If the mass of the object decreases by half, then the kinetic energy will ____________ by ___________. doubles increases a factor of 5 decrease half
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Kinetic energy can be solved by using the equation: KE = mv2 1 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. 22=4 If the velocity is quadrupled, then the kinetic energy increases by a factor of 16. 42= 16
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· half the mass gives 1/2 the KE, · double the speed gives 4 x KE · therefore (1/2)(4)= 2 A
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Imagine a roller coaster car that is at the top of the first hill and is stopped. Does the car stay stopped at the top
entire ride? What happens?
Once the car leans over the edge, gravity pulls it down. The ride is taking advantage
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
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
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!)
Work is required to elevate objects against Earth's gravity. For example, work is done on the truck to elevate it
truck is equal to the truck's gravitational potential energy at this new height.
Gravitational potential energy is determined by three factors: mass, gravitational acceleration, and height. All three factors are directly proportional to energy. Mass: The heavier the object is, the _______ gravitational potential energy the object has. Gravitational Acceleration: The larger the 'g', the _________ gravitational potential energy the object has. Since gravity on Earth is considered a constant, this will not change. Height: The higher the object is off the ground, the _________ gravitational potential energy the object has. more more more
h = 2 m h = 2 m m = 2 kg m = 1 kg
In this picture, the mass of a tennis ball was doubled when it was at the same height off of the ground.
How does the gravitational potential energy compare for the two objects?
h = 2 m h = 2 m m = 2 kg m = 1 kg
Mass: doubled Gravitational Acceleration: stayed the same, no change Height: stayed the same, no change Since the only thing that changed was the mass, which doubled, the gravitational potential energy also doubled.
h = 4 m h = 2 m
In this picture, a tennis ball is lifted to a height that is twice as high.
How would the gravitational potential energy compare at the higher height?
h = 4 m h = 2 m
Mass: stayed the same, no change Gravitational Acceleration: stayed the same, no change Height: doubled Since the only thing that changed was the height which doubled, the gravitational potential energy also doubled.
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Gravitational potential energy can be solved by using the equation: variable units Name
Gravitational Potential Energy
Gravity
Let's fill in the table below.
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/s2)(2 m) GPE = 9.8 J Click on the box to see the solution.
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GPE= mgh = 50 kg(9.8 m/s2)(10 m) = 4,900 J
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GPE= mgh = 3000 kg(9.8 m/s2)(100 m) = 294,000,000 J
GPE = mgh GPE = mgh GPE = mgh
If any of these decrease, then the GPE decreases by the same factor. 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.
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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?
Elastic potential energy is determined by two factors: the elasticity
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.
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
potential energy stored in it if it is neither stretched nor
state is shown in figure (a). Stretching a spring is caused when the spring is pulled increasing the length
the relaxed length, as shown in figure (b).
(a) (b) (c)
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.
(a) (b) (c)
relaxed stretched compressed no EPE stored
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. For each case, is elastic potential energy stored in the spring?
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Elastic potential energy can be solved by using the equation: EPE = kx2 1 2 EPE = Elastic Potential Energy (J) k = spring constant (N/m) x = distance of stretch or compression (m)
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?
A spring that has a spring constant of 10 N/m, is stretched a distance of 1 m from its relaxed length. How much elastic potential energy is stored in the spring? EPE = kx2 EPE = ( )(10 N/m)(1 m)2 EPE = ( )(10 N/m)(1 m2) EPE = (5 N*m) EPE = 5 J
1 2 1 2 1 2
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A spring that has a spring constant of 10 N/m, is stretched a distance of 1 m from its relaxed length. How much elastic potential energy is stored in the spring? EPE = kx2 EPE = ( )(10 N/m)(1 m)2 EPE = ( )(10 N/m)(1 m2) EPE = (5 N*m) EPE = 5 J
1 2 1 2 1 2
Click on the box to see the solution. Teacher Notes
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Please note that there are multiple ways to model the math of this
students at least two ways and then continuing to use the model that a majority of your students prefer.
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EPE= 1/2 kx2 = 1/2 (200 N/m) (0.25 m) 2 = 1/2 (200 N/m)(0.0625 m2) = 100 N/m (0.0625 m2) EPE = 6.25 J
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EPE= 1/2 kx2 = 1/2 (40 N/m) (0.5 m)2 = 20 N/m (0.25 m2) EPE = 5 J
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EPE = kx2 1 2 1 2 KE = mv2 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?
EPE = kx2
1 2
EPE is _________________________ to the spring constant. EPE is _________________________ to the square of the distance the spring is compressed or stretched. directly proportional directly proportional
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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?
Hint: think back to the roller
energy did it have at the top of the hill?
This is called the Conservation of Energy. initial Total Energy = final Total Energy TEi = TEf 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.
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. TEi = TEf 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!
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: (PE + KE)i = (PE + KE)f
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) When would KE be zero? · the object is not moving
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 1 m before being dropped. Use the idea of conservation of energy to determine the missing values. v= 0 m/s Height = 1 m Height = 0.5 m Height = 0 m Remember that the total mechanical energy at that position is the sum of the two individual energies: (PE + KE) TE = 0.5 J PE = 0.5 J KE = 0 J TE = 0.5 J PE = 0.25 J KE = 0.25 J TE = 0.5 J PE = 0 J KE = 0.5 J
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.
40 J 15 J 25 J
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
At position B in the diagram below, the roller coaster car has a gravitational potential energy equal to 15 J.
40 J 15 J 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
At position C in the diagram below, the roller coaster car has a gravitational potential energy equal to 25 J.
40 J 15 J 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? 15 J
h = 0 m
h = 0 m
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h = 0 m
h = 0 m
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h = 0 m
h = 0 m
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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 1 m again. Suppose the ball bounces after it hits the ground. What will happen to the KE? Just as potential energy can be transferred to kinetic energy, kinetic energy can be transferred into potential energy. v= 0 m/s Height = 1 m Height = 0.5 m Height = 0 m TE = 0.5 J PE = 0.5 J KE = 0 J TE = 0.5 J PE = 0.25 J KE = 0.25 J TE = 0.5 J PE = 0 J KE = 0.5 J
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! v= 0 m/s Height = 1 m Height = 0.5 m Height = 0 m TE = 0.5 J PE = 0.5 J KE = 0 J TE = 0.5 J PE = 0.25 J KE = 0.25 J TE = 0.5 J PE = 0 J KE = 0.5 J
In reality, the ball will not bounce as high as it was dropped. Does this mean energy was lost? v= 0 m/s Height < 1 m TE = 0.5 J PE = 0 J KE = 0.5 J NME = 0.10 J NME=0.10 J TE = 0.5 J PE = 0.25 J KE = 0.15 J TE = 0.5 J PE = 0.4 J KE = 0 J Sound Energy!
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!
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. Kinetic energy can also be transferred to elastic potential energy.
In the top picture, the block is travelling at 10 m/s, meaning that it has kinetic
therefore has no elastic potential
spring system is entirely due to the KE
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.
A B C
A B C
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If the total amount of energy that we start with, Ei, does not equal the total amount of energy that we end up with, "Ef", then energy was not conserved TEi TEf This means that there was an outside force that acted on the
considered the ball and the ground as the system together. What if we just considered the ball as the system by itself?
v= 0 m/s Height < 1 m TE = 0.5 J PE = 0 J KE = 0.5 J NME = 0.10 J NME=0.10 J TE = 0.4 J PE = 0.25 J KE = 0.15 J TE = 0.4 J PE = 0.4 J KE = 0 J Sound Energy! TE = 0.5 J 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
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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.
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!
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
energy) into electrical energy!
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
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!
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!
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 (CO2) when
considered a greenhouse gas, which many believe is a cause global warming.
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they convert mechanical energy into electrical energy