What is Gravitational potential: Definition and 388 Discussions
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance.
In mathematics, the gravitational potential is also known as the Newtonian potential and is fundamental in the study of potential theory. It may also be used for solving the electrostatic and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies.
Using taylor series expansion to prove gravitational potential energy equation, GMm/r=mgh at distances close to the earth.
R= radius of the Earth h= height above surface of the Earth m= mass of object M= Mass of the earth
U = - GmM/(R + h)
= - GmM/R(1+ h/R)
= - (GmM/R)(1+ h/R)^-1
do a...
I am a bit confused about gravitational potential energy near the earth, namely the formula given by mgh.
I know that potential energy is defined as U(x) = -W(x0 to x) where x0 is our chosen reference point. Let's take the Earth's surface as the zero point and let's travel upwards to a point...
Hi,
I am looking to use the definition from WGS84 to calculate Earth's gravitational potential using spherical harmonics, however I am having some difficulty finding the definition of one of the variables. Gravitational potential is given as the following:
V = \frac{GM}{r}\left [ 1 +...
I was wondering if dark energy might actually be gravitational potential energy.
If one assumes that space is flat and that the Universe is approximately a sphere with mass M and the Hubble radius R then we find that we have the approximate relation:
\frac{G M }{R} = c^2
A mass m...
Homework Statement
The mean diameters of Mars and Earth are 6.9 10^3 km and 1.3 10^4 km, respectively.?
The mass of Mars is 0.11 times Earth's mass.
(a) What is the ratio of the mean density of Mars to that of Earth?
(b) What is the value of the gravitational acceleration on Mars...
Is what I am currently reading about. The book I am reading presents it by giving an example; it proposes lifting a mass without any acceleration through a height, h, with an upward force equal and opposite to its weight. Does that mean the net work done on this mass is zero? My hand still does...
I have attached a discussion by R.Feynman where he derives the formula for gravitational potential energy using pure reasoning. I don't quite follow the reasoning and I have read the discussion many times yet can't get a grasp of things he says. With the discussion I have my doubts in red...
Hello Colleagues,
I am curious about a problem in Quantum Mechanics that incorporates the evolution of a Gaussian Wave Packet under the Gravitational Potential.
What I am interested in is equation (3) in the following paper:
"On the quantum analogue of Galileo's leaning tower...
Hey guys,
I'm currently trying to get my head around the concept of gravitational potential energy;
U_{r} = -\frac{Gm_{1}m_{2}}{r}
My question concerns whether this relates to both bodies in the system individually, or together.
That is, if I have two masses separated by a distance...
Homework Statement
What is the gravitational potential energy of a car with centre of mass at a height h above the ground? On a level road the centre of mass is at a height of 0.1m above the ground.
Homework Equations
gravitational potential energy=mgh
The Attempt at a Solution
I would use...
It sounds like an easy-enough problem, but even writing down the ridiculously nonlinear equation that would need to be solved is making my face hurt.
I'm talking classical/Newtonian gravitation, action-at-a-distance, constant-force. It could really be any external non-EM conserved force...
Hello all, I'm new to the forum here and desperately need some help in some basic physics concepts that I need to have a firm grasp on for the MCAT.
My question is about PE on an inclined plane. For example, there are 3 possible scenarios (the height and mass remains the same for each...
Just a little confused, when work is done on an object it's energy increases right? (i.e. Work done on object = Change P.E + Change K.E + Work done by object)
So how come when gravitational force does work on an object(i.e. it falls) the potential energy decreases instead.
So its like Work...
Why is gravitational potential energy relative to the height you set?
When I say relative, I don't mean anything having to do with relativity. Obviously as you go further from the earth, you have more potential energy but in the equation Ug=mgh if you set the height to 0 there is no potential...
Homework Statement
A piece of fruit falls straight down. As it falls,
A. the gravitational force does positive work on it and the
gravitational potential energy increases.
B. the gravitational force does positive work on it and the
gravitational potential energy decreases.
C. the...
Homework Statement
An archer places a 0.15kg arrow on a boasting. Then the archer exerts an average force of 100 Newtons to draw the string back 0.45 meters. Assume that friction is negligible.
A) what speed does the bow give to the arrow? (5 marks)
B) If the arrow is shot vertically...
Homework Statement
A 4.0 kg mass is pressed down on a vertical spring of spring constant 400 N/m, compressing it to 0.250 m. After it is released, the amount of kinetic energy this mass would have when it leaves the spring is ___.
Homework Equations
mgy(final) + 1/2 kx^2 (final) + 1/2...
Homework Statement
GRAVITATIONAL POTENTIAL AND FIELD DUE TO A “THIN” ROD
A thin rod of length L lies along the +y-axis, with one end at the
origin (see diagram).
Assume:
• The rod has length only- no thickness in other directions.
• The density of the rod increases proportionally to...
Feynman's lecture on physics: chapter 4 derives equation for gravitational potential energy by a "lifting 3 balls" example. The book notes:
"But the strange thing is that, in a certain way of speaking, we have not lifted two of them at all because, after all, there were balls on shelves 2 and...
1. From a solid sphere of radius R and mass M, a small sphere of radius R/4 is scooped out and placed on the surface of the original sphere on a diametrically opposite point as shown in the figure. The gravitational potential of the resulting system at a point P(as shown in the figure) is (Take...
Homework Statement
The gravitational self potential energy of a solid energy of a solid ball of mass density p and radius R is E. What is the gravitational self potential energy of a ball of mass density p and radius 2R?
Homework Equations
The Attempt at a Solution
The...
Hello,
I thought of asking would someone know what is the correct thinking here...
A body is thrown upwards, its kinetic energy gradually transforms into gravitational potential energy until it is entirely absorbed.
At this moment, where is the potential energy? According to wikipedia (N...
Homework Statement
A 1000kg roller coaster, with its passengers, starts from rest at point A( h= 9.5 m) on a friction track whose profile is shown in the diagram above at right.
a) what is its maximum speed?
b) with what speed does the roller coaster arrive at point e?
c) What constant...
In this question 3 bi
http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9702%20-%20Physics/9702_w07_qp_2.pdf
to find gravitaional poteintial enrgy we need to find Δh. which is the vertical difference between the two spheres shown in the diagram. How do i find that?
Answer...
Homework Statement
Question:
Rank the paths according to the corresponding change in the gravitational potential energy of the rocket–moon system, greatest first.
A. 1 > 3 > 5 > 2 = 4 = 6
B. 2 = 4 = 6 > 5 > 3 > 1
C. 1 = 2 = 3 = 4 = 5 = 6
D. 1 > 2 = 4 = 6 > 3 > 5
The Attempt at a Solution...
Explain how a skier can have more than one value for gravitational potential energy at anyone time?
My attempt at an answer.
Consider the position of the skier is relative to the bottom of the hill. Therefore the skier has gravitational potential energy as he/she descends down the hill. At...
Homework Statement
A rocket is propelled vertically upward from the Earth which has a radius R0. After
its fuel has become exhausted, the rocket reaches its highest point at a height of 2R0
above the surface of the Earth and then falls vertically down back to the earth. With
what speed...
In the Proof of the Gravitational Potential Energy Law , it says :
Consider two point masses , body . mass "m" and Earth mass "M" , where M remains fixed. The work done to move the mass "m" from point 1 to point 2 is given by :
W(1-2) = ∫FG . dr (All in vectors) = ∫FG Cos 180° dr ( All in...
In my book it is talking about conservation forces and work energy theorem.
In the book it said...
"suppose gravitational potential energy alone does work (constant force)
*Then Wnet = Wg ... ending statement Ef = Ei...
My question... Does the work energy theorem only deal with...
How gravitational potential effects mass?
Is this formula
m = m0/sqrt(1-Φ/c^2) right or at least close to reality?
The purpose of the question:
If overage Φ decreases because of Universe is expanding,
then maybe it can help to find another explanation why it expands with acceleration.
Lets...
Homework Statement
Find the potential and force on a mass m outside and inside the Earth in terms of g, the acceleration due to gravity, assuming Earth has uniform density and radius R.Homework Equations
For a mass m, the potential energy of it in the gravitational field of a spherical shell of...
Homework Statement
A marble is placed at the top of an inverted hemispherical bowl of radius R = 0.30 m. It starts from rest and slides down the bowl without friction. Draw a free body diagram when the marble reaches an angular position θ = 16.6°. From your FBD, sketch the approximate...
Hey guys
So if I lift a book from the ground it gains potential energy. I do work on the book and when I release it the potential energy that I gave the book pulls the book back down to Earth.
However I was looking at a potential energy formula for planets which was
V = -GMm/r
But...
Homework Statement
A 400-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy of the child–Earth system relative to the child’s lowest position when (a) the ropes are horizontal, (b) the ropes make a 30.0° angle with the vertical, and (c) the...
Homework Statement
Calculate the gain of potential energy of a mountaineer of mass 80kg who travels to the top of the mountain Everest 9km above sea level.
Homework Equations
ΔEp=mgΔh
The Attempt at a Solution
ΔEp=mgΔh=80x9.81x9x10^3=7.1x10^6J.
This is the correct answer but...
Homework Statement
An object is moved from A to B in the gravitational field of earth. The distance between the center of Earth and B is twice that of A. If the gravitational potential energy of the object at A is -2MJ, what is the gravitational potential energy of the object at B?Homework...
While trying to get my head around Gravitational Potential Energy I devised the following simple system:
Point Mass A of 1kg is 1000m away from Point Mass B of 100kg within an empty universe.
The gravitational force exerted by A on B is G*10^-16; by B on A is G*10^-4. At time=0 these two...
I want to propose that Gravitational Potential Energy (GPE) is a renewable energy input source but I feel maybe GPE might not be accepted as part of the surroundings acting upon the energy boundary of a system.
What are the rules of the energy boundary that umpire what is allowed and...
Hello, having had an interest in physics for a while I recently enrolled on an access to higher education course to study it. Unfortunately I seem to have fallen at the first hurdle. First off I'd like to apologise profoundly and profusely for the simple problem you are about to read, but I have...
This may have been answered elsewhere but I couldn’t find it. Is it the case that gravitational potential energy will add mass to an object the same way nuclear binding energy will?
In other words, as I move an object away from Earth is it gaining mass in the form of the stored energy I put...
Homework Statement
I have learned that gravitational potential energy's formula is:
GPE = mgh
But I saw other formulas relating to gravitational potential energy:
\phi = -G(m/r)
And then one formula like this:
F = dU(x)/dx
And then there's a formula relating to the CHANGE in...
In this investigation I had to calculate my maximum power as I run up a flight of stairs. These are a few questions that I have for my lab. I want to know if my calculations are right.
Given:
1. mass: 70kg
2. h = 1.17m
3. d= 1.78m
4. t = 2.02s
Use the information from 1 and 2 to...
Hey, I have a test tommorow and I don't really understand gravitational potential energy or kepler's laws. It's not really a theory test, it's the math aspect, but I still don't understand it. I know of the formulas such as Fg=Gm1m2/r^2, Eg=Gm1m2/r, Ek=1/2 mv^2, and I think that's all. But...
Homework Statement
Deep in space, two neutron stars are separated (center-to-center) by a distance of 18 X 106 km apart. Neutron star A has a mass of 153 X 1028 kg and radius 52000 m while the neutron star B has a mass of 159 X 1028 kg and radius 72000 m. They are initially at rest with...
A model rocket has a mass of 3.00kg. It is fired so that when it is 220 m above the ground it is traveling vertically at 165m/s. At the point its fuel runs out so that the rest of the flight is without power. Assume that the effect of air friction is negligible and that all potential energies...
Homework Statement
if the angle of the slope is increased, the change of gravitational potential energy between the two heights: (Select all that apply) (It may be more that one option)
increases
depends on the path followed.
decreases.
depends only on the difference between the two...
Homework Statement
[PLAIN]http://img818.imageshack.us/img818/817/potentialenergy.jpg
Homework Equations
Given above.
The Attempt at a Solution
I've never had physics in my life and am completely baffled by this problem. I'm only in calculus 3 and am just learning infinite...