0
votes
1answer
44 views

Computing average force exerted by ground when jumping

Problem: A man of mass $m$ jumps vertically into the air from a sitting position in which his center of mass (CoM) is at a height $h_1$. When his feet are just about to leave the ground his CoM is at ...
2
votes
1answer
91 views

Loss of gravitational potential energy in an infinitely far object

Now consider I went into a rocket which goes an infinite distance far from earth. By infinite I mean very far. The gravitational attraction between me and the earth will significantly decrease and ...
0
votes
1answer
64 views

Statements about gravitational potential energy contradicting intuition?

So in my textbook I am told: two masses have gravitational potential energy because work had to be done in order to move one the masses form a position very far away (lets say infinity) to the ...
5
votes
2answers
120 views

What is the energy required to create mass of m at a height of h above the Earth?

What is the energy required to create mass of m at a height of h above the Earth? Is it $E= m c ^2$ or $E = mc ^ 2 + mgh$ ? Let's reverse the process also. If you convert mass $m$ at $h = 0$ to ...
0
votes
2answers
301 views

How does potential energy work in the context of objects in space?

It's said that potential energy is "energy of position." If an object is sitting on a shelf five feet above the floor, its potential energy can be thought of as equal to the amount of energy that ...
7
votes
1answer
504 views

Does potential energy in gravitationall field increase mass?

I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a ...
1
vote
2answers
264 views

Negative potential energy of gravity

Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)? If so it seems to me that the ...
6
votes
1answer
226 views

Orbital mechanics and rocketry: Is it ever a good idea to intentionally lower periapsis?

tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at ...
-1
votes
1answer
74 views

Gravitational potential energy

Consider two places next to each other: Place 1, where there is a gravitational field whereas Place 2 - there's no field. Now if we lifted a box in place 1, it gains potential energy. Then, we move ...
0
votes
2answers
303 views

Measuring work done by gravity over non-constant gravitational acceleration

A question from an example from a MIT Classical Mechanics Lecture on Work. Here's the given definition for gravitational potential energy (~32:00): "The ...
1
vote
1answer
556 views

Derivation of the self gravitational potential energy of a sphere

I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
2
votes
2answers
551 views

Lever Mechanics - How to formulate an ideal lever launch

Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a ...
20
votes
8answers
3k views

Why are L4 and L5 lagrangian points stable?

This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the L1, L2, and L3 lagrangian points. The blue ...
3
votes
4answers
2k views

Does the mass of an object change as it moves away from the earth?

The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it ...
1
vote
3answers
1k views

Still trying to understand gravitational potential and Poisson's equation?

A week or so back I asked a question about the gravitational potential field $$\phi=\frac{-Gm}{r}, \qquad r\neq 0, $$ and how to show the Laplacian of $\phi$ equals zero for $r\neq 0$? Eventually, ...
1
vote
2answers
288 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...
3
votes
1answer
879 views

Trying to understand Laplace's equation

I'm struggling here so please excuse if I'm writing nonsense. I understand that the gravitational potential field, a scalar field, is given by $$\phi=\frac{-Gm}{r}$$ where $\phi$ is the ...
2
votes
1answer
427 views

Potential energy in a gravitational field

I've seen the following formula for the potential energy of a body in a gravitational field ($\rho$ is the density, $g$ is the gravitational acceleration): $$ \rho g \int_E z dV $$ Can you please ...