The usefulness of those definitions is the ease with which we can solve many problems using conservation of energy. A typical neutron star has the about the same mass as our sun, but a diameter of only 20km or so. m = 4Kg and v = ?. by Idayatidayat. ]cP7^IzbyCu_dN.L ^Z You might want to use this triangle to help you with questions involving potential energy. the energy to de-orbit one rod (the energy needed to change its orbital speed to zero) the gravitational potential energy of one rod relative to the surface of the Earth in joules in tons of TNT equivalent the impact velocity of a de-orbitted rod (disregarding aerodynamic drag and the rotational motion of the Earth) numerical Crash landing Gravitational Potential Energy - Introductory Example Problems. This is approximately 12% of the gravitational potential energy and just 3% of the kinetic energy needed for orbital velocity (4% of total energy required). The object present at a certain height will have energy saved in the form of potential energy. represents the gravitational potential energy. 9.3: Gravitational potential energy. Was this helpful ? How far away in light years is a distant quasar if it appears to be moving away from us at 90% of the speed of light? You may also wish to learn the formula in characters: GPE = mgh. A 1-kg body free fall from rest, from a height of 10 m. (b) The change in gravitational potential energy, Acceleration due to gravity (g) = 10 m/s2, Weight (w) = m g = (1 kg)(10 m/s2) = 10 N. The change in gravitational potential energy is equal to the work done by gravity. The following aspects of gravitational potential energy proved to be particularly important and useful: 1. xZYo8~7Gu)i`gfEv6<8@nwlO ~DvK}xXq`u|U|Y'fggu]f{v{O?O!dNo849>,"b2(oGG>";}x O3 Stream water at the top of the waterfall. Question 2: A mass of 5Kg is taken from the ground to the height of 100m. Thus, the potential energy of the object is 5000J. Laugh at your earliest convenience. PE g = KE. When the spring is kept normally, it is said to have 0 energy and is said to be in the equilibrium state. Work done against to the earth to elevate the objects is multiplication of its weight . A cart on the top of a hill; A roller coaster resting on its highest point; . Lessons for IGCSE Physics. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Fundamentals of Java Collection Framework, Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam. stream For example a stretched or compressed spring has potential energy. Related Practice. Calculate the speed needed to escape the Milky Way from our solar system. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/s 2.Since the zero of gravitational potential energy can be chosen at . This energy is due to motion. 1 0 obj In daily use, the potential word is used a lot for things or persons which show promise inside them. The initial location (i) is point A, and the final location (f) is point D. If the height at C is 0 meters, then the height at A is 24 meters, and the height at D is 12 meters. <> Gravitational energy is potential energy stored in an object based on its distance from the Earth. School Guide: Roadmap For School Students, Data Structures & Algorithms- Self Paced Course, Difference between Gravitational Potential Energy and Elastic Potential Energy, Difference between the Gravitational Potential Energy and Gravitational Potential, Difference between Kinetic Energy and Potential Energy, Difference Between Electric Potential and Potential Difference, Stress, Strain and Elastic Potential Energy. Mechanical, Potential and Kinetic Energy wx = w sin = (10)(sin 30o) = (10)(0.5) = 5 N, W = F d = w h = (10 N)(1 m) = 10 N m = 10 Joule. <> q 1 and q 2 are the charges. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Ep = m g h, Gravitational Potential Energy - IGCSE Physics. Answer: The potential energy of a mass 'm' at the height 'h' is given by, P = mgh Given: m = 2kg and g = 10 m/s 2 and h = 10m. What keeps you to the ground is the earth's gravity and it causes objects to fall. The following are the gravitational potential energy examples: Lifting heavy weights. Gravitational potential energy means when the potential energy is been witnessed due to the gravitational force been applied. The potential energy of two charged particles at a distance can be found through the equation: (3) E = q 1 q 2 4 o r. where. With decreasing height, velocity increases, and it acquires kinetic energy. 0 = 8.85 10 12 C 2 / J m. For charges with the same sign, E has a + sign and tends to get smaller as r increases. . Mass (m) = 1500 gram = 1500/1000 kilogram = 1.5 kilogram, Wanted : The gravitational potential energy, PE = m g h = (1.5 kg)(10 m/s2)(20 m) = 300 kg m2/s2 = 300 Joule. E p m g h Example: A box has a mass of 5.8kg. The mass of the Earth is 5.9 1024 kg and mass of the Sun is 1.9 1030 kg. (Your answer to this question can also be used to determine the age of the universe.). = m*g*h . r is distance. 9 views . An objects gravitational potential. For the sake of simplicity, assume you are a sphere with a uniform density equal to that of water and a mass equal to your mass today. Perform the following set of calculations. Usually, potential energy is released by an object by motion. Example Problem 1 - Solving Potential Energy Problems What is the gravitational potential energy of a 12-lb bowling ball being held 0.56 meters above the ground on Earth? Solution The gravitational potential energy U ( r ) can be calculated by finding the sum of gravitational potential energy of each pair of particles. of the helicopter? Step by Step Science. The gravitational force is a conservative force. Home; AP; Class; Defenition; Problem; University; About Us; Contact Us; What are 3 examples of gravitational potential energy? endobj This problem involves the conservation of energy. Given: m = 5kg and g = 10 m/s2 and h = 5m. Thus, the potential energy of the object is 250J. Question 3: A mass of 5Kg is taken from the ground for 5m uphill on the wedge. If you were a black hole what would be the radius of your event horizon? (1 kg = 2.2 lbs) This is the energy stored in the gravitational field of an object. A ball with a mass of 500g is lifted onto a shelf which is 1.5m above the ground. So over here, if gravity can do let's say 100 joules of work in moving that ball down, then we will say the gravitational potential energy is 100 joules. Which object has more Potential energy if the first object is 5 times heavier than the second? If the Earth were a black hole what would be the radius of its event horizon? Potential energy (PE) is energy that an object has because it is at a location that is higher than its surroundings. A kid at the top of the slide. The total energy is then given by E = T + Ui = - 1.251010 Joules. Known : Change of potential energy (PE) = 4900 Joule Mass of object (m) = 50 kg Acceleration due to gravity (g) = 9.8 m/s2 Wanted: height (h) Solution : PE = m g h Acceleration due to gravity (g) = 9.8 ms-2. Potential energy is put into work due gravitational force presence. Hence, the only things you need to calculate GPE are the mass of the object and the height of . Gravity is a force that pulls two objects toward each other. Gravitational potential energy: PE g = mgh (or U g) Here, m is the mass of the object, g is the gravitational field, and h is the . 2 0 obj By how much does a meter of space expand in ten years? The initial kinetic energy is the one with the known velocity that was given, since it was projected downward with a given speed, while m g d sin. Water retentive to a dam. Thermal energy from friction. Lets see some problems based on these concepts. Fruits on the tree. Difference Between Mean, Median, and Mode with Examples, Class 11 NCERT Solutions - Chapter 7 Permutations And Combinations - Exercise 7.1. If all the kinetic energy becomes We know that work done by a force F on a displacement s on the object is given by. The wedge makes an angle of 30 with the ground. by Jsteer. July 25, 2021. Potential energy is stored energy from an object. Using the equations for PEg PE g and KE, KE, we can solve for the final speed v, v, which is the desired quantity. Example Question #1 : Gravitational Potential Energy A lazy contractor of mass 80kg who is bricking a building figured out that a seesaw makes his life much easier. Gravitational potential energy is energy an object possesses because of its position in a gravitational field.The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/s 2. The most common use of gravitational potential energy is for an object near the surface of the Earth . A raised . What is the gravitational potential energy of the object. A series of free GCSE/IGCSE Physics Notes and Lessons. Question 7: The entire potential energy of a ball is transformed into its kinetic energy by coming on the ground from a certain height. Question 1: A mass of 2Kg is taken from the ground to the height of 10m. Therefore, the final gain in kinetic energy is 98 Joules. . Then on the right side, which is where I'm confused, the kinetic energy is 0 because the block has momentarily stopped. Gravitational potential energy 1. Determine the release height that would give a 5g marshmallow the same kinetic energy as a small, one kiloton nuclear bomb (4.210, The 1969, Apollo11 mission to the moon was. Learn what gravitational potential energy means and how to calculate it. x#7;Kufo8y@ Related Pages A boy throws a 0.2kg rock up with a speed of 5m/s. 5. Question 6: Find the velocity of the ball just before hitting the ground. Wanted: Comparison of potential energy of object 1 and object 2, m = mass (its international unit is kilogram, abbreviated kg), g = acceleration due to gravity (its international unit is meter per second squared, abbreviated m/s2), h = height (its international unit is meter, abbreviated m), PE = gravitational potential energy (its international unit is kg m2/s2 or Joule). Where, x= displacement, K= Spring constant. Calculate the gravitational potential energy gained by the ball (g = 9.8 N/kg). Problem 1: Calculate the potential energy of a 1.5 kg book which is about to fall from the top of a 2.65 m bookshelf. Show that the gravitational potential energy of an object of mass mm size 12{m} {} at height hh size 12{h} {} on Earth is given by PEg=mghPEg=mgh. problem solver below to practice various math topics. Figure 1. They have met with legal, political, economic, and scientific skepticism. Here, m is the mass of the object, and v is its speed. The formula for the gravitational potential energy between two objects is: U=GMmr , where U is the gravitational potential energy in J , G is the . (a) The work done to lift the weight is stored in the mass-Earth system as gravitational potential energy. Energy Keywords Balloon pop. The potential has units of energy per mass, e.g., J/kg in the MKS system. Support Materials Standards Vocabulary Segment E: Kinetic Energy and Gravitational Potential Energy From Physics in Motion, Unit 4 Segment E: Kinetic Energy and Gravitational Potential Energy The product GM is the standard gravitational parameter and is often known to higher precision than G or M separately. It is the capacity of gravity to do work. gained by the mass (g = 9.8 N/kg). Word Problems On Gravitational Potential Energy scientific instruments have you ever been in the middle of a class lecture medical examination or episode of star trek only to realise suddenly that you have no clue what all those gizmos . By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero. AP Physics 1- Work, Energy, & Power Practice Problems ANSWERS FACT. Some. The questions on this page test your ability to use the formula: Change in GPE = mass gravity change in height. Possible Answers: Correct answer: Explanation: The equation for potential energy is . the gravitational potential energy of one rod relative to the surface of the Earth in joules in tons of TNT equivalent the impact velocity of a de-orbitted rod (disregarding aerodynamic drag and the rotational motion of the Earth) solution The orbital speed of the platform Fc = Fg v = 5210 m/s The orbital period of the platform in hours and minutes He needs to deliver bricks to his coworker who is 10 meters above him. Its orbit encloses a mass that is 78 billion times the mass of the Sun.). Elastic Potential Energy Practice Problems Problem 1: Calculate the elastic potential energy of a spring when it is stretched from 0.15 m to 0.30 m. (Take the value of spring constant, k = 150 N/m) Solution: Given data: Elastic potential energy of a spring, U s = ? It also has some initial gravitational potential energy associated with its position on the surface Ui = - = - 6.251010 Joules. Acceleration due to gravity is 10 m/s. If all the masses are equal, then m1 = m2 = m3 = m4 = M The gravitational potential V (r) at a point O is equal to the sum of the gravitational potentials due to individual mass. Conservative forces. (Hint: they came back to Earth when the mission was over.). We will look at which factors effects the magnitude of potential energy or which does not effect. Gravitational Potential Energy Heat Engines Heat Transfer Efficiency Kinetic Energy Mechanical Power Potential Energy Potential Energy and Energy Conservation Pulling Force Renewable Energy Sources Wind Energy Work Energy Principle Engineering Physics Angular Momentum Angular Work and Power Engine Cycles First Law of Thermodynamics If the ball is dropped, in that case, the potential energy decreases, and the speed increases. When it is stretched or compressed, and there is a certain displacement, say x, it will have certain potential energy saved in it which is given as. Find the potential energy of the object. Find the potential energy of the object. They have been described as hypervelocity rod bundles, orbital telephone poles, and most poetically rods from God. Gravitational potential energy may be converted to other forms of energy, such as kinetic energy. Energy Transfers b. ST4l%n do. Gravitational acceleration, g = 9.81 m/s 2 Try the free Mathway calculator and About how big is this? Note that we plugged in for because the ball will be moving downward; the change in height is negative as the ball drops. It gives an idea of stored energy that can be converted. The work done against the gravitational force goes into an important form of stored energy that we will explore in this section. Calculate its potential energy. The height at which the ball was initially placed was 10m. A kid at the summit of a park slide. How much work gravity can do. Problem 1: A mass of 5 kg is raised from the ground to a height of 8 meters. Energy can take on many forms and can be converted from one form to another form. The Earth, the Sun, planets and stars all produce significant amounts of gravity. Question 4: A mass of 10Kg is taken from the ground for 10m uphill on the wedge. Work as area under curve. The potential energy of a mass m at the height h is given by. are some examples of different types of energy. 0 A crane lifts a 75kg mass a height of 8 m. Calculate the gravitational potential energy Instead of coming from motion, it can come from its position relative to others, internal stress, electric charge, or its condition. Kinetic energy: KE = mv2. 1. Work example problems. This energy is said to be stored inside the object. (The sun is 25,000 light years from galactic center halfway to the edge of the galaxy. The Earth to Sun distance is around 150 million km. 4 0 obj %PDF-1.5 Elastic Potential Energy So what would be gravitational potential energy? Find the value of Potential energy stored in the spring? The following physics revision questions are provided in support of the physics tutorial on Gravitational Potential Energy. Let's find the \( \vec{g} \) field due to a sphere of constant mass density \( \rho \), using the gravitational potential \( \Phi \). It's a number which tells how much work you can do. ). The initial kinetic energy is given by 1/2mv2 = 1/21000 (10000)2 = 51010 Joules. Gravitational potential energy is calculated as follows: E p = m g h Examples: A crane lifts a 75kg mass a height of 8 m. Calculate the gravitational potential energy gained by the mass (g = 9.8 N/kg). Gravitational potential energy is energy an object possesses because of its position in a gravitational field. Question 1. This means the potential energy of the object is getting converted to kinetic energy. Gravitational energy is the energy associated with gravity as you may think. Find the gain in the kinetic energy. External force in the form of gravity is acting on it. Where m is the mass in kilograms, g is the acceleration due to gravity(9.8 m/s 2 at the earth's surface) and . Besides, according to physics, energy is something that . For example, a stretched spring, when released, starts moving towards its natural position and starts acquiring speed. Kinetic Energy is calculated by the following variables: 1/2 x Mass x Velocity^2. Given: m = 2kg and g = 10 m/s2 and h = 10m. Hide transcripts. Given the values in the table, determine the following quantities for a hypothetical, hypervelocity, orbiting, rod bundle system, the object's recessional velocity (usually stated in km/s), the object's distance from the Milky Way (usually stated in megaparsecs or Mpc), a constant of proportionality known as the. calculated as follows: Repeat this problem for an out of control satellite at the same altitude above the moon. 3 0 obj % Power. What was the escape velocity from the Earth at the altitude of the final burn of the third stage of Apollo11? What is the gravitational potential energy of the object. Let's see some problems based on these concepts. A 1-kg body free fall from rest, from a height of 10 m. Determine : (a) Work done by force of gravity (b) The change in gravitational potential energy Acceleration due to gravity (g) = 10 m/s2 Known : Mass (m) = 1 kg Height (h) = 10 m Gravitational potential (V; the gravitational energy per unit mass) at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object. This concept is an integral part of mechanics and allows us to theoretically measure the energy stored inside an object. Compute the critical density in terms of hydrogen atoms per cubic meter. Gravitational potential energy - problems and solutions by Alexsander San Lohat 1. 2. Gravitational Potential Energy; Gravitational Potential Energy, Example Problems. because we've already seen that if we have multiple sources of gravity (or any conservative force), the total potential energy \( U \) is just the sum of the . This wedge is in the form of a right-angled triangle. examples of gravitational energy and elastic potential enrgy showing top 8 worksheets in the category Earths surface. Potential energy is the energy possessed by an object due to its position or configuration. How do their current speeds compare to the escape speeds you calculated? Therefore, even when the first object is kept at lesser height, due to its weight, the first object has more potential energy. The equation for gravitational potential energy is: GPE = mgh Where, m is the mass in kilograms g is the acceleration due to gravity (9.8 on Earth) h is the height above the ground in meters Also Read: Gravitational Force Kepler's Laws Gravitational Field Intensity Derivation of Gravitational Potential Energy Equation Question 5: Find the kinetic energy of the ball just before hitting the ground. Question 9: A spring is stretched upto 9cm, the spring constant of the spring is 2N/m. Gravitational energy is a form of potential energy. Potential energy, electric potential energy, kinetic energy, etc. Energy 4900 Joule used to raise an object with mass of 50 kg to a height of h. What is the height of h? Substituting this equation into equation (1) we get. We shall see few examples regarding gravitational potential energy to electrical energy. Gravitational potential energy True or false. Find the potential energy of the object. where g is the acceleration due to gravity near Earth's surface, h is the height relative to your reference point, and is the cart's velocity. To further understand this, lets consider a ball of mass m. The mass of the ball is 1 kg. How to Add a Page Border in Microsoft Word. If the Sun were a black hole what would be the radius of its event horizon? This energy could be mechanical energy, chemical energy, electric energy, nuclear . It is the potential energy stored by an object because of its higher position compared to a lower position. Work/energy problem with friction. Are the numbers you just calculated reasonable; that is, would spacecraft with these initial conditions really hit the surface at these speeds? 4. (Hint: Use the formulas for escape velocity, the Hubble law, and the density of a uniform sphere.). Suppose an object is stable on the ground, now by applying some energy, it is taken at a certain height. For example, the lowest height in a problem is usually defined as zero potential energy, or if an object is in space, the farthest point away from the system is often defined as zero potential energy. Examples of Gravitational Potential Energy: Car on top of hill; Image Source: explainthatstuff Once the vehicle starts descending down the hill, it develops velocity which transforms the potential energy into kinetic energy. b. a) calculate the gravitational potential energy of the book relative to the ground Gravitational Potential Energy. Kinetic energy comes when the object starts moving. Will the universe continue expanding forever or will gravity eventually cause it all to collapse in a big crunch? Gravitational Potential Energy, Example Problems - YouTube Gravitational potential energy is the energy stored in an object due to its position. Due to the state in which object is present. There are some well-accepted choices of initial potential energy. Electric potential Energy Match up. When the ball is about to hit the ground, its potential energy has become zero and all the energy is converted into kinetic energy. Given that one parsec equals 3.0856810. The loss of gravitational potential energy from moving downward through a distance h h equals the gain in kinetic energy. (b) As the weight moves downward, this gravitational potential energy is transferred to the cuckoo . by Ssimkin. (Hint: it's less.) Examples of Potential Energy Problems Study these sample problems and the methods used to solve them. This is due to the force of gravity acting on an object. What is thermal energy? The total PE of an object is equal to the mass (m) of the object multiplied by the height (h) of the object above the ground. In fact, mathematically, it is calculated based on the following formula: mass x gravitational acceleration rate (9.8 m/s^2) x height. Since, the all the potential energy present in the ball is transferred into its kinetic energy, Potential energy of the ball = Final gain in the kinetic energy. the energy to de-orbit one rod (the energy needed to change its orbital speed to zero), the gravitational potential energy of one rod relative to the surface of the Earth, the impact velocity of a de-orbitted rod (disregarding aerodynamic drag and the rotational motion of the Earth), Determine the impact speed of an out of control satellite initially at rest falling from an altitude of 3.510. Derive an expression for the critical density of the universe. where G is the gravitational constant, and F is the gravitational force. . When the ball is about to hit the ground, its potential energy has become zero and all the energy is converted into kinetic energy. The following diagram gives the formula for gravitational potential energy. When it is dropped, it starts going towards the ground and its height starts decreasing. But, potential energy is difficult to explain because there is no movement in potential energy.. <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> What is the gravitational potential energy of an object on the ground? The difference in gravitational potential energy of an object (in the Earth-object system) between two rungs of a ladder will be the same for the first two rungs as for the last two rungs. the page for more examples and solutions on how to use the formula. The box is lifted from the garage floor and placed on a shelf. Then, the potential energy, with respect to zero at r 0, is just U ( r ). Report an Error Gravitational potential energy and kinetic energy are defined and explained mathematically through multiple example problems. Then, work done by gravity on the object is. Hence m g x sin. Examples of Gravitational potential energy. Calculate the amount of gravitational potential energy gained by an object raised above ground level. A neutron star is the collapsed core of a star that has gone supernova. It is given as. Potential energy is energy that is stored in an object or substance. A boy has a mass of 55 kg. Solution: The distance between sun & Earth R= 150 million km = 150 1011m. Gravitational energy is a form of potential energy. Speculate on the fate of the universe given that the mean density of a galaxy is roughly one hydrogen atom per cubic centimeter while the mean density of the space between galaxies is about one hydrogen atom per cubic meter. What is the Difference between Interactive and Script Mode in Python Programming? Anderson Video - Potential Energy and Gravity. This video goes through the basics of what gravitational potential energy is . The contractor puts bricks on one side of the seesaw and jumps on the other side to fling the bricks upward. Lets say the speed of the ball just before touching the ground is v. <>>> Assume that initially, the ball was at a height of 100m, and its mass was 4Kg. This object has the capability of producing energy as these conditions change. They were also used as a plot device in the 2013 action-adventure movie GIJoe: Retaliation. Although this energy is due to motion, this energy is not created. R&gPe*xIlP&'*yxp"%Tr? i!b_2vUW,4$0=2R4-@-eYv>\jXO!%o/oilxRk{.v:];9[eO AP Physics 1- Work, Energy, & Power Practice Problems ANSWERS FACT WebGravitational potential energy: PE g = mgh (or U g) Here, m is the mass of the object, g is the gravitational field, and h is the vertical height of the object above its lowest position. problem and check your answer with the step-by-step explanations. Sample Problems Question 1: A mass of 2Kg is taken from the ground to the height of 10m. An automobile is parked on a hilltop. Potential energy is energy that is stored in an object or substance. How does the actual speed of the spacecraft at the end of the burn compare to the escape velocity? Based on figure below, if mass of object 1 is 2 kg and mass of object 2 is 4 kg, comparison of potential energy of object 1 and object 2 is .. Embedded content, if any, are copyrights of their respective owners. Copyright 2005, 2022 - OnlineMathLearning.com. Find the potential energy of the block. 7 views . A yoyo before it is released. Plugging the values in the formula. A ball with a mass of 500g is lifted onto a shelf which is 1.5m above the ground. Learn what gravitational potential energy means and how to calculate it. Gravitational Potential Energy, Example Problems | Pearson+ Channels 10. Calculate the escape velocity of the Sun at the current locations of Voyager1 and Voyager2. We welcome your feedback, comments and questions about this site or page. Question 10: Two objects are kept at different heights, first object is at 5meters and second object is placed at 15 meters. Gravitational energy is potential energy stored in an object based on its distance from the Earth. Potential shows the possibility for action. Water at the top of the waterfall. Speculate on the fate of the universe given that the Hubble constant appears to be increasing. These two examples of gravitational and spring potential energy are calculated differently. Gravitational Potential Energy - Introductory Example Problems. Science, 28.10.2019 16:29, Laurenjayshree What socio economic condition shaped him? Calculate the speed needed to escape the Sun from the Earth's orbit. Some energies are easier to understand and imagine while some are hard to explain or understand. Explain the significance of this comparison for the flight of Apollo11. An object sitting at some height possesses potential energy due to height. Hydroelectric Dam Gravity Battery Falling Electric Toy Car Differences in potential energy are the measurable and physically significant quantities associated with gravitational potential energy. This is the idea behind potential energy. In this case, force is the force of gravity and displacement from the ground to the height h. Thus, the potential energy of the object is 125J. There are lots of gravitational potential energy examples in real life. This can be rewritten as. Schemes like this have been in the works in the United States since 1964 (under the informal name of Project Thor) and are revived from time to time for example, by the RAND Corporation in 2002 and by the US Air Force in 2003. The gravitational potential energy of object 1 : The gravitational potential energy of object 2 : Comparison of the potential energy of object 1 and object 2 : , free fall to the ground. 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