What is Gravitational potential energy: Definition and 290 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.
If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2?
I...
Hello everyone! I noticed in the derivation of potential energy, Mr Lewin defined the gravitational potential energy of a mass m at point P relative to a much larger mass M. He says the potential energy of m at point P is equal to the work he would have to do to move the mass m from infinity to...
My attempt:
Let ##M_e## be the mass of the Earth and ##M_m## be the mass of the person. Let ##D_{EM}## be the distance from Earth to Mars and let ##R_e## be the radius of the earth.
Defining these constants (leaving off units for brevity):
Masses in Kilograms (G is not a mass but I'll leave...
A question to physicists: What sort of real world scenario / image would *best* depict the increase in gravitational potential energy in a radial field?
Would a rocket traveling through the Earth's atmosphere suffice or are there better alternatives?
This image would have to be relevant to the...
Here is my solution, which is correct.
The tilt of the water at the top can be described in terms of ##x## and ##y## as ##y = \frac{2y_0}{L}x##. The height of the water at any given x is then equal to ##h + \frac{2y_0}{L}x## where ##x \in [-\frac{L}{2}, \frac{L}{2}]##.
So the potential...
Hi,
If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal...
Good day,
If I consider my system to be an object and the earth, and the object is on the surface of the earth, then the system will have gravitational potential energy. Why couldn't I say that only the object (considering it as my system) has gravitational potential energy?
Thanks
First, in section 20.4, after listing all the things gravitational potential energy does not do, they say the equivalence principle forbids it being localized. I thought I understood the equivalence principle, but maybe I don’t. Any comments explaining that would be appreciated.
Second, they...
Hi,
When regarding Gravitational Potential Energy, I know the formula is U=mgh. However, when the object is on an incline (say at an angle of 52 degrees) would it still be mgh or something else? (This isn't homework I simply was just curious).
Hi,
I am confused about the negative aspect of these quantities. The definition in my book for gravitational potential is:
"The work done to move a unit mass from infinity to a point in a gravitational field"
I understand that the work done is negative because gravity is doing the work if you...
hello I would like some help with the first part of this homework.
for the moment i have done this:
E initial=m*g*h
Efinal= 1/2 m*v ^ 2+1/2I*ω ^ 2
Ei=m*g*h+1/2I*ω ^ 2
Ef=1/2*m*v ^ 2
my doubt is with the potential energy since it confuses me when there is or not...
I'm reading Schutz's A First Course In General Relativity and in chapter 5 he discusses an idealized experiment in which an object is dropped from a tower, then turned into a photon and sent back up to its original height.
In classical mechanics we would say that as the object falls it loses...
the gravitational potential energy of a body at any point is defined to be negative of the work done by the conservative force(gravity in this case) from bringing it to that point from a given reference point. if the reference point is taken to be at infinity and the potential energy at this...
Spring has more potential energy when it is compressed or stretched from its initially balanced state. As external work is done, it stores energy in the form of potential energy. Here, we know energy is stored in spring but For the Earth-ball system, where the energy stored?
(Throughout all my post, I will refer to “gravitational potential energy” just as “potential energy”)
Hi! I have this confusion about when is potential energy positive/negative and how it is related to how we define our axes. I think it is easier to understand my confusion with the following...
Gravitational energy is the potential energy a physical object with mass has in relation to another massive object due to gravity, so, does an object outside a gravitational field have no gravitational potential energy?
For example, the Earth is 4.5 billion years old, so it's gravity stretches...
Homework Statement
The change in gravitational potential energy of a mass m as it moves from the surface to a height h above the surface of a planet of mass M and radius R is given by:
ΔPE= GMmh/R(R+h)
a) show that when h is very small compared to R , this approximates to the more familiar...
Homework Statement
Let's consider two wooden logs. We burn the first one at the base of the mountain and the second one on the peak. Which one is releasing more energy? Do they release the same amount of energy?
Does the potential energy affect the burning
Homework Equations
## \Delta H =##...
Can someone please show that calculation of gravitational potential energy at a point R+h from the centre of the Earth by choosing the centre of the Earth to be at zero potential. Here R is the radius of the Earth and h is not very small wrt to R
I am hoping to get a deeper understanding of the difference between two different gravitational potential energy equations, the first of which is given by
U = mgh
and the second given by
U = (Gm1m2)/r
I first assumed that in a system consisting of the Earth and, say, a tennis ball, these...
Anyone know if the following statement is true (and why)?
"Getting to higher ground would increase his gravitational potential energy, decreasing the effects of non-conservative forces, which would allow him to move easier."
CLARIFICATION: "move easier" refers to a lack of friction and not the...
Homework Statement
Project Thor is a proposed (and terrifying) weapon system where a cylindrical tungsten rod (19600 kg m3 ) about the size of a telephone pole (6.10 m long and 0.300 m in diameter) is dropped from Earth orbit. Imagine you dropped one of these from an orbit 10,000 km above the...
Homework Statement
Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...
Homework Statement
I'm trying to solve problem a problem of complete energy of doubled pendulum (2 mathematical pendulums connected by a string).
For a kinetic energy I would get (1/2) J(w_1)ˆ2 + (1/2) J(w_2)ˆ2 and for a potential energy of a spring (1/2) k (ϕ_1-ϕ_1)
What about gravitational...
Homework Statement
Two Jupiter sized planets are released from rest 1.0 X 10^11 m apart. What are their speeds as they crash together?
I think my problem lies in figuring out which radius to use. In an equation like this are the radii of the planets included in the distance between them...
The gravitational potential energy of two massic points ##P_1## and ##P_2## with respective masses ##m_1## and ##m_2## is given by
$$U = -G \frac{m_1 m_2}{|| P_2 - P_1 ||}$$
Now I was wondering how this formula could be applied to continuous matter. Let us imagine a very simple case where we...
I am no able to understand the reasoning of Feynman in deducing that it is impossible to build a machine that will lift a weight higher than it will be lifted by a reversible machine. I am also not able to understand what reversible machine is. So, please help me.
Is it necessary to be the kinetic energy greater than gpe to move ( I don't talk about in orbits)
Example :
Is it will be harder to move an object has a bigger gpe ( same mass but bigger hight from ground).
And thanks.
Homework Statement
Q7. Some lead shot with a mass of 50 grams is placed into a card board box the distance from one end to the other being 1m. The ends are sealed with rubber bungs in order to prevent the lead shots from falling out, the tube is rotated so the lead shots fall down from one end...
Homework Statement
What % of PEg must be converted in KE in order to double the speed of a pendulum? So I have spent a couple of days trying to figure out this problem (it's a lab), and I can't seem to figure it out. I have asked my physics teacher about it, and he said the answer to the...
Hi guys. I'm new to this forum so I'm not sure if I'm posting this in the right place or correctly, but I was totally stumped on a Physics 12 question as I was studying for my exam.
The question is:
An explorer spacecraft is descending towards Mars using a rocket engine for braking. The...
I have two simple examples of potential energy and kinetic energy.
First example: Imagine a book on the ground and I want to lift it.At first I apply a force just a little more than the gravitational force of the Earth so that it has some velocity. After the book gets that velocity, I keep my...
Homework Statement
Hi,
Infinitely far away from a mass-->gravitational potential is zero.
As get closer-->becomes negative.
At surface-->it is the smallest value of r, i.e. the radius of the mass, hence the most negative value for gravitational potential.
But as you go below surface of Earth...
If my understanding is correct, all particles are sources of gravitational fields (albeit minor ones), and the gravitational potential energy between two bodies is given by:
U = -GMm/r
So, if we have two Z bosons (or any other bosons with mass but no repulsion due to charge) which are traveling...
Homework Statement
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In a movie stunt, a 65 kg skier starts from a rest position at the top of a hill 30 m high. She slides down the hill to the bottom, where she collides with a 45 kg stationary skier. The collision is completely inelastic. Find the final velocity of the skiers.
Homework...
X has a mass of 55 kg and hangs from a rope. As a result of this the rope stretches by 0.6 m. Calculate the energy stored in the rope as a result of stretching.
Solution:
F = kx and E = 0.5x^2. Using this fetches the answer as 161.5
However, the change in potential energy (calculated using mgh )...
Homework Statement
Question :-
Two stars, each of a solar mass and radius ##10^7 m## are at a distance of ##10^{12} m## from each other. Find the speed of each star before collision if initial speed is negligible.
Homework Equations
$$V(r) = {-G Mm \over r}$$
The Attempt at a Solution...
Homework Statement
A teeter toy is composed of a massless central stick of length L and two massless sticks of length l attached at angles α, each with a mass m at the end (see the figure). We imagine tilting the toy by an angle θ from the upright position.
a) Find an expression for the...
1. A comet that passes by Earth has GPE, which will be all lost if it begins to fall towards Earth. If it's shot back up, it will now start with Ek and finish with a higher GPE.
Now, what exactly is this GPE? if energy cannot be created or destroyed, but transformed, where does it get stored at...
I know that when an object A a does positive work on another object B, object A loses energy and object B gains energy(there is transfer of energy from object A to object B) and when object A does negative work on object B, it gains energy and object B loses energy(there is transfer of energy...
I am currently reading Gravitational Curvature by Theodore Frankel. In the derivation of Einstein's equations in chapter 3, he states that the gravitational potential energy of a blob of fluid is
∫B½p0U√gVdx
where the integral is a volume integral, p0 is the rest energy density and √gvdx is...
Homework Statement
A body of mass m is taken at a constant speed from the surface of the Earth (radius = Re) to infinity.
(a) What is the work W1 done on the body in the process?
(b) If m is taken from a distance r > Re to infinity, how much work W2 is required?
(c)Which quantity is larger, W1...
Does the rest mass of an object increase when it acquires gravitational potential energy, and if so, is this the reason why Einstein believed that the inertia of a mass increases in the presence of other masses?
Hi Guys,When we are finding the wasted energy when something is dropped a tower, we do this: mgH-0.5mv^2
My question is, does the velocity of the kinetic energy have to be vertical component, or can it be the impact velocity when it hits the ground?
Thanks
Hello, I do not quite get this. Can anyone provide examples?
" We may feel that it takes a force greater than the weight of the object being raised to lift it upwards, but it is not so. Provided the force is equal to the weight, the object will move upwards at a steady speed. "