What is Gravitation potential energy: Definition and 38 Discussions

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J.
The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, and does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work.

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  1. D

    B Conceptually understanding change in potential energy with 0 net work

    Suppose somehow an object is moving upwards with a speed ##v##, at this point I start applying a force ##F## that is equal to its weight, so the net force on the object is zero. So it will continue moving upwards with its initial speed. Suppose after the height difference is ##h##, I stop...
  2. sachin

    Variation of escape velocity with equal surface gravity

    the question says "There are two Planets, each with the same surface gravity, but Planet 1 has a greater radius and is less massive then Planet 2. Which of these planets has a greater escape velocity? " (A) Planet 1 (B) Planet 2 (C) Both have the same escape velocity because surface gravity is...
  3. Priyo137

    Escape Velocity from Earth starting from its Centre

    What is the minimum velocity (theoretically) of an object located at the CENTER of the Earth to move it outside its gravitational field?
  4. Penny57

    Oscillation of bead with gravitating masses

    The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...
  5. slogals

    Two black holes moving in a circular orbit around a point

    I tried solving it and i was able to do a) and b) here is what i did on c), but its not correct according to the solution
  6. D.S.Beyer

    B Density of the early Universe contributing to the red-shift?

    Does the relative density of the early universe contribute to the red-shift of distant galaxies? If so, by how much? How would this be calculated? Asked another way : Assuming both the early universe and the current universe are flat, could the relative difference of their space time metric...
  7. harambe

    What Is the Maximum Angle Attained by a Particle Projected from Earth?

    Homework Statement A particle is projeccted from the surface of the Earth with an initial speed of 4km/s.Find the maximum angle attained by the particle.Radius of the earth=6400km and g=9.8m/s2 Homework Equations KE1+U1=KE2+U2 [/B]The Attempt at a Solution So I tried to proceed by this...
  8. G

    B How Is the Coefficient of Restitution Linked to Conservation of Energy?

    Where does the Coefficient of Restitution equation come from, in terms of the Conservation of Energy? The measure of efficiency is the velocity after the collision divided by the velocity before the collision, but how does it get to that point? I'm trying to view this focused on an object that...
  9. G

    Stuck on projectile motion problem using gravitational force

    Homework Statement A projectile is fired vertically from the Earth's surface with an initial speed of 11.4 km/s. Neglecting air drag, how far (in meters) above the surface of the Earth will it go? Homework Equations (1/2)mv^2 -GmM/R The Attempt at a Solution KEi+PEi = KEf+PEf (1/2)mv^2 -...
  10. V

    Examples of conversion of gravitational PE to heat energy?

    Homework Statement I was looking for some examples where gravitational potential energy is converted to heat energy. Are there many such examples of this conversion? I could only come up with one such example and even that could be an incorrect example. Homework Equations PEg = mgh The...
  11. Garlic

    Problem on a question about the gravitation potential

    Hello everyone 1. Homework Statement In the solution of a question, regarding the gravitational force fields and gravitational potential when the mass is inside Earth (where the height of the mass is lower than the radius of earth), the step where we take the integral of the force in order to...
  12. Cocoleia

    Find gravitational potent. energy - isotropic distribution

    Homework Statement I am told that the gravitational force of a mass m located inside an isotropic distribution of spherical radius R and total mass M is given by Fg = -GmM(r)/r^2 where r is the distance between m and the center of distribution and M (r) is the mass contained below the distance...
  13. A

    Can someone help me please - Velocity and GPE and Forces

    Homework Statement Explain why the velocity at time of impact was much higher than the average velocity Explain why the actual gravitational potential energy will in reality be much higher than this Explain why increasing the time of impact would mean the rocket was less likely to get...
  14. ThinkerCorny

    Understanding gravitational potential due to spherical shell

    I know that gravitational potential due to uniform sherical shell at a point outside the shell is equivalent to the potential due to particle of same mass situated at the centre and got proof here http://m.sparknotes.com/physics/gravitation/potential/section3.rhtml. But I was looking for more...
  15. N

    Conservation of energy: Conceptual question

    Homework Statement Two identical twins, A & B, are riding identical bikes up the same hill, both at constant speed. Twin A takes 20 seconds to climb the hill, while twin B takes 40 seconds. a) Neglecting all forms of friction, which twin consumes more energy? b) With friction, which twin...
  16. A

    Gravitation energy of a spherical shell

    I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##. Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give...
  17. tink7718

    Initial height of a bouncing ball and energy lost

    I am doing a lab in my senior physics class (IB HL Physics 3-4) and I am very confused about a relationship that I found. For my experiment I dropped a racquetball from different heights and then used video analysis to find the height of the ball on its final bounce. I used this data to...
  18. i_hate_math

    A really confusing question on potential energy,

    Homework Statement A 975 g block is released from rest at height h0 above a vertical spring with spring constant k = 410 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 24.2 cm. How much work is done (a) by the block on the spring and...
  19. M

    Working out speed, kinetic energy and resistive force

    Homework Statement Homework Equations [/B] The Attempt at a Solution a) I'm not sure how to calculate speed without having both distance and time but I believe it will revolve around calculating gravitational potential energy and kinetic energy. bi) I think this is just simply using the...
  20. J

    Potential Energy of Nearly Hovering Rocket

    I have a question concerning gravitation potential energy and rockets under an unusual situation. Let a rocket be in a gravity well of a massive object such as a planet. For simplicity, assume that the rocket is in a vacuum. (we can add air effects later). The rocket engine thrust is dynamically...
  21. S

    I with Potential Energy compared to energy used.

    your going up hill in a big truck ,18 wheeler at a (*10 % Grade) or (* 5.7106 DEGREES) your fully loaded at (*80,000 lbs) or (*36287kg) or (*40 short tons) your traveling at (*30 mph) or (*13.41120m/s) you travel for about (*10 miles) or (*1609.344 Meters) the actual distance traveled would be...
  22. P

    How do I find rotational energy for a pulley system?

    Homework Statement So I have a horizontal pulley positioned at the edge of table with a mass of .2kg hanging down from a height of .76meters, the other end of the string is attached to a wooden block of mass .25kg that when the .2kg weight is dropped the wooden block is pulled towards the...
  23. S

    Dot product in the Gravitational Potential Energy formula

    This is the gravitational potential energy formula $$U = -\int_\infty^r\vec{F}_\text{field}\cdot d\vec{r}$$ If r vector's direction is form infinity to r, then it means it has same direction as Gravitational Force. So cos0=1 But after multiplication there is a negative sign here: "-GMm" $$U =...
  24. S

    Positive work while lifting an object

    According to work formula $$ W = \mathbf F\cdot\Delta\mathbf x $$ and $$ W = F\Delta x\cos\theta $$ If an object falls: F = Gravitational Force = negative Delta x = Final Position - Initial Position = negative ==> (Like 2 - 5 = -3 ; because it is falling) cos 0 = 1 ==>(because x and F have...
  25. S

    Velocity of an object Rotating in vacuum , Gravity applies

    I was wondering what might happen If we for instant, Rotated a ball around an axis in a vacuum chamber. First, If the initial speed was 20m/s would it remain like that forever, hypotheticaly saying No friction exists and that Air Resistance does not exist as the Ball rotates in vacuum. Also...
  26. 2

    Why is kinetic energy due to a planet's rotation treated as negative?

    Homework Statement I am trying to answer the following question: Among the animals that appear in the zoo of the Universe there are black holes and neutron stars. The mass of each of these is often the order of the mass of the Sun. The radius of a neutron star is about 10 km and a certain...
  27. 2

    Differential gravitational force causing tides model?

    Homework Statement Homework EquationsThe Attempt at a Solution For a), I initially tried to consider the component of the gravitational force of the moon acting normally to the Earth's surface. This would be F=F_0 cos(theta) where theta is the angle between a horizontal line going through A...
  28. M

    Gravitational potential energy: derive expression for energy

    Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...
  29. shounakbhatta

    How does the formula for gravitation potential energy work?

    Hello, Can anybody please explain me: While going through gravitation potential energy, I came across: F=G.m1.m2/r^2 From there it follows: g=-GM/r^2.r How does it follow? Specially the -G case? -- Shounak
  30. L

    Change in gravitation potential energy in space

    Homework Statement an object of mass 750 kg is lifted from the Earth's surface to a height of 6.8 x 10^6 m above its surface. Calculate the change in gravitational potential energy for the object. The Attempt at a Solution I used this formula ΔEg = Eg2 - Eg1 ΔEg = -(GMm/r2) -...
  31. M

    Equation for Gravitation potential energy

    So I was looking at the equation for Gravitation potential energy U = - Gm1m2/r This implies the energy is 0 as r→∞ However, if I lift a book above my head, wouldn't it have more potential energy than if it was lying on the ground, meaning as r (h) increases, potential energy increases? Where...
  32. D

    Gravitation Potential Energy Problem of WHY?

    Gravitation Potential Energy Problem of WHY? Homework Statement Energy is required to move a 1540 kg mass from the Earth’s surface to an altitude 3.12 times the Earth’s radius RE. What amount of energy is required to accomplish this move? The acceleration of gravity is 9.8 m/s^{2}...
  33. S

    What Is the Reason for Reversing hf-hi to hi-hf in Roller Coaster Physics?

    Gravitation Potential Energy Problem pls help! I would greatly appreciate help on a couple questions I have. I have been sic for the past few days and unable to go into school to ask my TA's questions. My first question is when should use the equation Ki + Ui = Kf + Uf or Kf -Ki = Uf - Ui ? I...
  34. J

    How Is Gravitational Potential Energy Calculated for a Skier on a Ski Lift?

    Homework Statement A 68.5-kg skier rides a 2.56-km ski lift from the base of a mountain to the top. The lift is at an angle of 13.9° to the horizontal. Determine the skier’s gravitational potential energy at the top of the mountain relative to the base of the mountain. Homework Equations Eg=...
  35. B

    Need Help on Gravitation Potential Energy Problem

    [SOLVED] Need Help on Gravitation Potential Energy Problem Homework Statement (a) A 5.3 kg particle and a 3.0 kg particle have a gravitational attraction with a magnitude of 2.6 x10^-12 N. What is the gravitational potential energy of the two-particle system? (b) If you triple the...
  36. N

    Gravitation potential energy without hieght

    1. A 55.5 kg skateboarder starts out with a speed of 1.75 m/s. He does +80.0 J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is...
  37. K

    Gravitation Potential Energy Help

    Calculate the ratio of the energy that would be required to put a mass M into orbit near the Earth's surface (if there were no friction) and the energy to put the same into distant space. I'm stuck. How am i suppose to calculate the ratio. I know the that the energy to put M into orbit near...