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...
Homework Statement
Example 5.3 from The Marion Thornton book (fifth edition) of Classical Dynamics states the following problem:
Consider a thin uniform circular ring of radius a and mass M. A mass m is placed in the plane of the ring. Find a position of equilibrium and determine whether it...
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...
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...
Gravitational potential energy between 2 objects is ##-{G\times M\times m\over R}.##
My question is, does the value of this equation of this equation mean total gravitational potential energy of both objects ?
i.e, say the gravitational potential energy of object with mass ##M## is ##p## and...
Homework Statement
What is the gravitational potential both inside and outside a spherical shell of inner radius b and outer radius a?
Homework Equations
φ = ∫g⋅da = -4πGMencl
g = d∅/dr in the r hat direction
The Attempt at a Solution
I can get as far as getting the gravitational field for...
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 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...
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...
Hello!
Let's say our gravitational potential is (as usual for 2 body),
$$a = -\frac{\mu}{r^3} \mathbf{r}$$.
Then the gradient of this is G,
$$\frac{\partial G}{\partial \mathbf{r}} = G = \frac{\mu}{r^3} [3 \hat{\mathbf{r}} \hat{\mathbf{r}}^\top - I] $$
Now if we take two time derivatives of...
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. "
Homework Statement
Consider the equations for electric potential energy:
and gravitational potential energy:
GPE=m*g*h
In the case of GPE, the potential energy increases as the distance between the two objects increases. This makes sense (to me), as the greater distance between the Earth...
Suppose the mass of planet is" M" and there is body in its surface whose mass is "m" and the field strength is "g" . If the body is thrown 1800 m then Gravitational Potential energy = mg(1800). My question is why can't we use formula GPE= GMm/x ? This is also the formula for gpe but why...
Homework Statement
Homework Equations
ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf)
where
G = gravitational constant
M₁ = mass of one object
M₂ = mass of the other object
Ri = initial distance
Rf = final distance
ΔPE = -ΔKE
The Attempt at a Solution
My solution is v = 2√(GM/d). I am making sure it is...
Homework Statement
A 400-N child is in a swing that is attached to a pair of ropes 2.00 m long. Find the gravitational potential energy of the child-Earth system relative to the child’s lowest position when
(b) the ropes make a 30.0° angle with the vertical
Homework Equations
Ug=mgy
The...
Hi all, I am very confused about the graphs of gravitational potential and gravitational field strength...
I know that both gravitational field (g) and electric field strength (E) are negative gradient of their corresponding potential (Vg and Ve). If so, shouldn't g and Vg graph look very much...
Homework Statement
Two neutron stars are separated by a distance of 4.80 E 10 m. They each have a mass of 3.60 E 30 kg and a radius of 1.30 E 5 m. If they are initially at rest...
How fast is each star moving when their separation has decreased to half its initial value?
How fast is each star...
This pertains to a homework question but I get the concept of PE or U = -GmM/a for an elliptical orbit. I also understand the derivation of the total energy of an object in an elliptical orbit as E = -GmM/2a. However, I have a homework question that asks for the ratio of an object's kinetic...
Homework Statement
An 18.5kg box is slid up a 5.6m long ramp that makes an angle of 33 degrees with the floor. What is the gravitational potential energy of the box relative to the floor?
Homework Equations
Ek = 1/2mv2
The Attempt at a Solution
My teacher gave me an answer of 550J, but I'm...
In my textbook, gravitational potential , V=-(GM)/r, has been evaluated by applying calculas. I want to evaluate it with another simple way except calculas. I want to learn the simplest way to evaluate it in such a way that even a boy of 12 years old can understand it without facing any difficulty.
Hi everyone I'm kinda new here, your support will really be appreciated ! :D
1. Homework Statement
Let's say the cylinder has radius R, and height T.
Homework Equations
U = ∫GmdM/x
The Attempt at a Solution
My attempt is shown in the picture, I took a tiny element of the cylinder with...
Homework Statement
How do we define an electrostatic potential? My teacher tried to explain it through teaching us gravitational potentials, and I have presented what I came up with under '3.The attempt at a solution'. Please see below and thanks in advance for any help in clarifying whether my...
Homework Statement
Why is the gravitational potential energy of a ball a distance r from the center of the Earth negative?
Homework Equations
U_\text{grav}(r) = - GMm/r
[/B]
(To me, this makes sense because gravity is an attractive force and bodies will want to minimize the distance between...
In the context of a project, I had to solve numerically Poisson equation with cylindrical coordinates. I put here results for z = 0 on a 3D mesh 256x256x256.
Below 1 figure representing the final solution (in absolute value) in the case of a galaxy; I use the CGS units for the potential.
I...
So say I had a glass of water on a table ,with the glass filled to the top. The bottom of the glass, the water would have a higher pressure than the top of the glass. This is the concept of hydrostatic pressure etc.
But how does GPE fit into all of this? Does the water at the top of the glass...
Hello, here's a questions I was wondering if any of you could solve. I don't have the exact numbers, but the scenario is this: a guy standing on the Earth throws a ball upwards and catches it a few seconds later.
How does would affect the potential energy and/or mechanical energy of the...
Homework Statement
I am having a hard time understanding where to begin with this problem. Here it is:
Consider a thin rod of length L and constant density n that lies on the x-axis with endpoints at x=0 and x=L.
(i) Find a formula for the gravitational potential Φ = Φ(x) at the (variable)...
Homework Statement :[/B]
"Calculate gravitational potential at point Z, which is 8.10 x 107m away from a planet of mass 1.08 x 1023. "
(This point is between the planet and a moon, where the gravitational field strength is zero. I'm not sure if that makes a difference. The moon's mass is 4.8 x...
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 =...
I am reading a textbook about potential theory,
it mentions that a uniform sphere has 'dependence' on its gravitational potential, in terms of spherical harmonics.
[ite
I don't understand the term dependence? What does this mean exactly?
Cheers
If two masses that are separated by a distance are created from pure energy using the equation E=mc^2, where did the gravitational potential energy between them come from? Does this mean the speed of light isn't really constant, and must be changed very slightly to accommodate it? Could it be...
Homework Statement
A uniform cord of length .25 meters and mass .015 kg is initially stuck to a ceiling. Later, it hangs vertically from the ceiling with one end still stuck. What is the change in gravitational potential energy of the cord with this change in orientation?Homework Equations
Ug...
Homework Statement
A projectile is fired vertically from Earth's surface with an initial speed of 3.1 km/s. Neglecting air drag, how far above the surface of Earth will it go?
Homework Equations
KF+UF=KI+UF
U=-G(M1m2)/r2
K=1/2mv2
mass of Earth = 5.972E24
radius of Earth = 6371km
G=6.673E-11...
Homework Statement
The definition of gravitational potential at a point in my textbook is "the work done per kg to move a small test mass from infinity to that point"
I am having difficulty grasping this concept,
how is work done bringing an object closer to earth??
shouldn't work be done...
Homework Statement
For a satellite of mass ##m_s## in a circular orbit of radius ##r_s## around the Earth, determine its kinetic energy K.
Homework Equations
## K = \frac {1}{2}mv^2 ##
Gravitational potential energy ## U(r) = - \frac {GmM_E}{r}##
The Attempt at a Solution
My answer is ## K...
Homework Statement
[/B]
Calculate the gravitational potential energy of the interacting pair of the Earth and a 23kg block sitting on the surface of the Earth. You would need to supply the absolute value of this result to move the block to a location very far from the Earth
(actually, you...
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...
Homework Statement
A broken spaceship is located h=10 km above the center of a large circular thin sheet of unknown dust. The sheet has a radius of R=106 km and a density of σ = 7*1011 kg/m2. The spaceship and the dust attract each other due to the gravitational force.
a) Find the initial...
In this case the height of the fall is far to high above Earth to be use PE=mgh. So I'm trying to integrate the inverse square gravitational force over distance.
##\int \frac{GmM_e}{r^2}dr##
So I'm confused with respect to another object, specifically the moon, if the max height of the fall...
I understand that GPE is negative, but it does not come out this way when i try to derive it. I took the change in potential energy in bringing a particle from an infinite distance to a distance of b from another particle.
## \Delta U = - \int \vec F \cdot d \vec r ##. Since the...
Homework Statement
So I'm calculating the gravitational potential of a sphere at at point P. R = radius of sphere, r = distance from center of sphere to point P. I'm looking at two scenarios; r > R (1) and r < R (2). So I have the following integral:
\begin{equation} V(r) = \int...
Homework Statement
Forty 2.0kg blocks 20.0cm thick are used to make a retaining wall in the backyard. Each row of the wall will contain 10 blocks. You may assume that the first block is placed at the reference level. How much gravitational potential energy is stored in the wall when the blocks...
I tried to get the potential from the potential energy and I get a positive sign for potential...! I cannot find what I did wrong.
- Gravitational force is conservative so its work W is symmetrical to the change in potential energy U.
- Potential is the work done by gravitational force, per unit...
Homework Statement
Homework Equations
g = G*M / r^2, where g is the gravitational field strength, G is the gravitational constant, M is the mass of the attracting body, r is the distance from the center of mass of the body.
V = -G*M / r, where V is the gravitational potential.
The Attempt...