What is Gravitational energy: Definition and 67 Discussions
Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (converted into kinetic energy) when the objects fall towards each other. Gravitational potential energy increases when two objects are brought further apart.
For two pairwise interacting point particles, the gravitational potential energy
U
{\displaystyle U}
is given by
U
=
−
G
M
m
R
,
{\displaystyle U=-{\frac {GMm}{R}},}
where
M
{\displaystyle M}
and
m
{\displaystyle m}
are the masses of the two particles,
R
{\displaystyle R}
is the distance between them, and
G
{\displaystyle G}
is the gravitational constant.Close to the Earth's surface, the gravitational field is approximately constant, and the gravitational potential energy of an object reduces to
U
=
m
g
h
{\displaystyle U=mgh}
where
m
{\displaystyle m}
is the object's mass,
g
=
G
M
E
/
R
E
2
{\displaystyle g=GM_{\text{E}}/R_{\text{E}}^{2}}
is the gravity of Earth, and
h
{\displaystyle h}
is the height of the object's center of mass above a chosen reference level.
Electrons flowing through a resistor are dissipating electrical energy. The electrical energy is transported from the battery to the electrons along the curved field lines of the Poynting vector. It seems like a meaningful idea that electrical energy necessarily travels from the source to the...
Hello!
I was wondering if it is possible to express the gravitational energy as a product of the gravitational field by a moment, as we do with the magnetic and electric energy? Would this require the existence of bodies with negative mass? How could we relate this to the existence or total...
Hi,
Gravitational energy in de Sitter has equation of state w=-1 (cosmological constant) and w=-1/3 (curvature energy in open or closed de Sitter). Is this just gravitational radiation, and how does this accord with the equation of state of photon radiation w=1/3?
Does this mean that densities...
Homework Statement
Not give any information just the equation Fg= G m1m2/r^2
Supposed to find the distance at which the moons gravity has a greater force on a spacecraft than the Earth does.
Homework Equations
My prof told me to put G m1m2/r^2= G m1m2/r^2 and substitute one r in for another...
Hello everyone! I am a moderator over at the VS Battles Wiki, and I have some questions I believe one of y'all can answer. Basically the question is: how much energy does it take to destroy a star? We find this with GBE, but I have some questions as to calculating this value.
As far as I am...
Homework Statement
I have a 100 lb mass that is attached to a disk which is rotating freely about an axle. How do I calculate the gravitational energy contributed buy this 100 pound mass as it rotates from the 12 position to the six position
Homework Equations
No clue maybe. M x g x h?
The...
Homework Statement
I know that potential gravitational energy is relative to the reference point that I decide to choose (like in the picture below).
But then if, for instance, I set my reference point in the ceiling and my vertically down y-axis to be positive. What would the potential...
Hello! I hope this is the proper forum for my question(s). English is not my native language, so I apologize in advance for language mistakes.
In Feynman Lectures on Physics, there is a chapter about the conservation of energy. The first part, which deals with the definition of energy, I...
If a conduction band is placed in a current loop with gravitational waves acting upon it in parallel direction. It is also assumed that all the basic conditions relating to frequency are met for parallel propagation case as per gravitational wave damping papers below.
Since nuclear precession...
Homework Statement
"In Fig. 8-33, a runaway truck with failed brakes is moving downgrade at ##130\frac{km}{h}## just before the driver steers the truck up a friction-less emergency escape ramp with an inclination of ##θ=15°##. The truck's mass is ##1.2⋅10^4kg##. What minimum length L must the...
Homework Statement
The longest homerun hit by Miguel Cabrera in the 2012 season occurred at Comerica Park and had an initial y-component of velocity of 19.8 m/s and an initial x-component of velocity given as m/s, where is some value left undetermined.
Assume the ball left the bat 1.22 m off...
Homework Statement
Suppose that a 15 M(solar masses) star finally runs out of nuclear fuel in its core and undergoes a Type II supernova explosion. You are going to analyse the energy budget, calculating all the quantities in Joules.
a) Estimate the amount of gravitational energy that would be...
Homework Statement
"How much energy is released when a sphere of constant density (p) with mass (M) and radius (R) is put together gravitationally? What you should do is to think of the energy released when a shell is brought in from infinite distance (where potential energy of zero) to the...
Here is the question with two parts
The fastest that a human has run is about 12 m/s.
a) If a pole vaulter could run this fast and convert all of his or her kinetic energy into gravitational potential energy, how high would he or she go? 7pts
b) Using the 1990 pole vault world record of 20...
Homework Statement
1. What is the gravitational energy (relative to the unstretched surface of the trampoline) of the 20kg ball at its apex 2.0m above the trampoline
2. What is the kinetic energy of the ball just before impacting the trampoline
3. At maximum stretch at the bottom of the motion...
Homework Statement
Spaceship mass=450000kg Initial Velocity= 300m/s y + 400m/s z
Asteroid mass = 2000kg Initial Velocity= -100m/s y - 50m/s z
Speed after 498m/s
Question: If the force between the objects is 5000N, how long will it take for spaceship to capture the asteroid? (Assume...
First of all, I did not major in Physics, but I did pass GCE with A. (This is to make a point, not to boast.)
But there's a matter that doesn't make any sense to me, and none of my acquaintances could give me the clarification so I came to this forum, hoping someone can make me understand this...
If you view free fall as an inertial frame and therefore items at "rest" on the Earth's surface are accelerating away from the centre of mass I do not understand how energy is conserved. Taking this view, relative to the free fall frame the items will be gaining velocity which implies that the...
For centuries we have been using the gravitational potential energy of water courses by building watermills and dams with hydroelectric plants. The weather does the job of bringing the water back 'upstairs' for free so conceptually that's a wonderful energy source. The problem is (I guess) that...
Is the height in the formula the vertical distance from the bottom to the center of gravity of object, or is it just the vertical distance from the bottom to the very top of the object.
I mean..
If there is a sphere with mass m and radius r and placed at height h, what is its potential...
1. Imagine two objects, A and B, answer the questions that follow based on the conditions given.
A= 500g, at 2m, B=1.0kg, at 1m
a. Which has a greater Gravitational Energy? Why
b. If they are both dropped, which would have a greater velocity impact...
In nature, all forces have a limited value, i.e, their effect is reduced if many objects are influenced by that force. Example, the magnetic force experienced by a single iron nail (in a magnetic field) is greater than that of 2 iron nails in the same field.
Consider gravity,
gravity exerts...
We know that gravitational energy is negative (zero energy universe theory). If the mediator particles (bosons) of the gravitational interaction are gravitons, then the energy of the gravitons would be negative?
I'm not sure if I'm right ..
Here's my thought:
1. The First Law of Thermodynamics is the only single law which could derive energy formula. Furthermore, we can't, solely, use Newton's law to derive Kinetic Energy. It will make us fail to explain the existence of thermal energy.(*)
2. In...
How do you derive the equation for gravitational force from the eqauation for potential gravitational energy: e=-Gm/x? For me it seems as though you take the derivative and that would work, but i don't understand why it does?
If you draw a graph representing the tapering of gravitational force with respect to distance between two point masses (by the inverse square law y=x<exp-2>), the gravitational energy between two points would be the area under the graph between those points. This is my assumption.
Now the...
Homework Statement
I had a question regarding the elastic potential energy of a spring to the gravitational force of a cart. If you had a spring that was attached to the top of the inclined plane and to a cart with the cart moving downhill on an incline that was at an angle, how would...
Homework Statement
There are two equations from which change in gravitaton potential energy of a system can be calculated.
ΔEg = mgh and the other Eg = GmM/R
The first equation is only correct if the gravitational force is constant over a change in height h. The second is always correct...
It seems to me that gravitational bodies radiate gravitational energy continuously, without losing mass/energy. It that true?
Here are my reasons for thinking as such.
First of all, when I say “radiate” I just mean that in a general way. I don’t mean radiation as in electromagnetic...
Homework Statement
I am 65 kg and eat a 500 Calorie lunch and go hiking up a mountain afterwards. Assuming that chemical energy is converted to gravitational potential energy with 50% efficiency, approximately how many miles up the mountain can I go before I need my dinner?
0.5 miles...
In those two links it is written that gravitational energy does not exist.
http://arxiv.org/abs/0908.3322
http://fqxi.org/community/forum/topic/1371
1. I read these articles, but how it is possible to say more clearly that gravitational energy does not exist?
2. What this means on an example...
Acceleration -- all the energy is gravitational what speed was the ball thrown at?
Homework Statement
A ball is thrown up in the air and reaches a height of 2.2m assuming that all the energy is gravitational what speed was the ball thrown at.
Homework Equations
I cannot find the...
hello. i recently came across this question in which a satellite is put into orbit at a point around a planet with velocity 1.2V, where V is the speed for a circular orbit at that point and they ask for ratio of max to min distance. [Ans. 2.57]
what i want to know is how do we relate...
My semester project is to create a device that will make a sound at 5,10 15, and 20 seconds exactly using only gravitational energy.
-My initial design used two rotating axles with two gears through them and a chain. It would begin by me dropping a weight attached to one of the axles making it...
Homework Statement
A 70 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 13 m , and falls a total of 37 m .
Calculate the spring stiffness constant of the bungee cord, assuming Hooke's law applies.
Homework Equations
0.5kx^2 (final) +...
Homework Statement
Welcome to the Australian Physics course! I have to analyse the effects of changes on gravitational energy and radiation from the Sun on a manned spaceflight to Mars. I doubt my abilities to solve simple problems, however, so I now turn to the vast collective of the...
Homework Statement
a frictionless roller coaster car of mass m = 954 kg tops the first hill with speed v0 = 24.2 m/s at height h = 30.8 m. How much work does the gravitational force do on the car from that point to (a) point A. (same height)
Homework Equations
The Attempt at a...
Hello, the concept of potential gravitational energy seems very confusing to me, and it leads me to several questions, and I was wondering if some of you could explain this energy conceptually to me perhaps based with these questions as guidelines.
Potential gravitational energy increases...
Consider the uncertainty principle:
dp * dx = hbar
For photons we have the relation:
E = p c
Substituting into the above uncertainty principle:
dE = hbar c / dx (1)
As we look at a smaller and smaller piece of the zero-point field the (positive) energy diverges.
But...
Homework Statement
a) A watermelon with a mass of 2.0kg falls out of a tree house that is 5.4m above the ground. What is the speed of the watermelon just before it hits the ground?
First I found Eg to be 105.9 J based on the formula Eg = mg (h2 - h1).
Since the watermelon hits the...
I chanced upon an argument in Misner, Thorne and Wheeler to the effect that the energy/momentum of the gravitational field cannot classically be localised. Basic idea: you can make the Christoffel symbols vanish at any point, and hence the gravitational field at that point will vanish, taking...
1. A 6.5 kg ball is launched upwards from the ground with a speed of 21 m/s. If all of the ball's kinetic energy is converted to gravitational potential energy, how high will the ball go?
Given:
m = 6.5kg
v = 21m/s
Ek = 1433.25 J
g = 9.8 N/kg [down]
Required:
h =?
Solution...
When I multiplied angular accelaration with surface area of sphere .I got an equation for energy.
What do this equation mean by?
Is this equation describe gravitational energy?
A dim but resourceful student has a summer job in a factory moving boxes. The 50 kg student finds that if he runs at a speed of 5.8 m/s and then dives head first into the boxes, he can move them across the floor. If the boxes have a mass of 65 kg and the force of friction between the boxes and...
I have been thinking a bit about gravity in the classical Newtonian sense. So we know that the gravitational potential energy is inversely proportial to the distance that an object is from the object it is being attracted to. Thus if we form spheres of equal distance from a certain object we can...
Suppose you separate two masses from each other and expend a certain amount of energy in doing so, where exactly has this energy been transferred to?
I was thinking perhaps the mass of both objects increases much like how separating protons from a nucleus makes them heavier, but then that...
Homework Statement
1.) How fast must a rocket leave the Earth’s surface to reach a maximum height of 895 km above the surface of the Earth (assume the rocket is simply going straight up)?
The answer is 3920 m/s
2.) How fast must a rocket leave the Earth’s surface to reach an orbit with...
Homework Statement
A spherical star of uniform density p and radius R is formed by the condensation of the interstellar dust from large distance due to gravitational forces. Find the energy change that occurs at some intermediate stage as the radius increases from r to r+dr
Hence derive an...
[b]1. In a double-star system, two stars of mass 6.0 *10^30 kg each rotate about the system's center of mass at a radius of 2.0 * 10^11 m.
(a) What is their common angular speed?
(b) If a meteoroid passes through the system's center of mass perpendicular to their orbital plane, what minimum...
Homework Statement
So this was a long question recently given on my exam, and I had only a slight idea of how to do it.
A block of wood is 1.05m above the ground, and there's a ledge supporting it, and its just sitting there. A pendulum that weighs 200g. When it is pulled back, it is 0.73m...