All Questions
16
questions
0
votes
2
answers
119
views
In physics, what is the difference between a fact and a definition?
For example, I came across this statement:
"It is a fact that the components of force are derivatives of potential energy, but it is not a definition."
What does this statement mean?
I ...
- 77
0
votes
2
answers
362
views
What does potential energy really mean?
I have a lot of doubts regarding the potential energy definitions
First of all,I would try to express my Understandings(they might be wrong)regarding the issue
I was told that if Work done on a body ...
- 452
-1
votes
1
answer
116
views
How does one prove that the conservative force $\vec{F}$ is equal to the negative gradient of the potential $V$?
I have a grasp of the gradient theorem, and I understand that if we let $\phi$ be a function such that $\vec{F}=\nabla \phi$, and $V(\vec{x})$ be the potential at $\vec{x}$, then
$$-\int _C\vec{F}d\...
- 379
0
votes
1
answer
376
views
Why is $f = -\frac{du}{dx}$?
I am studying Newtonian Mechanics and I am familiar with single variable calculus.
I came across the concept of conservative and non conservative forces and potential energy. Here is what I understand:...
-3
votes
1
answer
61
views
Is energy, as we know it, "persistent"? [duplicate]
Suppose I raise a ball (with my hand) to some height. I am doing some work against gravity and storing potential energy in the ball.
However, once I loosen my grip, or just sweep my hand away from ...
- 71
5
votes
1
answer
352
views
Understanding conservative forces
I'm trying to better understand conservative forces. I have a decent intuitive idea of what they are, but I've recently learned the mathematical rigor behind it which has made me have some questions. ...
- 3,200
1
vote
3
answers
98
views
Understanding the equation for Potential Energy
I am having a hard time understanding why Potential Energy can be calculated in the following way:
$$ \Delta U = U_f - U_i = -\int_{x_i}^{x_f} F_x dx $$
In particular, I don't understand why there ...
- 35
0
votes
2
answers
1k
views
How has the definition of gravitational potential energy been derived?
The definition of gravitational potential energy is - The gravitational potential energy of an object at a point above the ground is defined as the work done is raising it from the ground to that ...
0
votes
2
answers
113
views
A More General Potential Energy
It occurred to me this morning that the notion of work and of spatial potential energy can be generalized to a more abstract form. In particular, work can be defined in terms of an abstract force ...
- 236
-2
votes
1
answer
79
views
Clarification of the definition of potential at a point
My textbook defines the potential at a point to be equal to the work done in bringing a unit positive charge from infinity to that point, and then explains that the point contains another unit ...
- 101
-1
votes
1
answer
152
views
Is this a good description for potential energy?
The potential energy can be seen as the energy stored in a system that can be "expelled". An object at a height $h$ above its reference point has a potential energy given by $U_{gravitational} = mgh$.
...
- 99
-1
votes
3
answers
128
views
Does raising an object fastly gives more potential energy than if it were raised to the same height slowly? [closed]
If we raise an object fastly we apply more force so more work is done and eventually potential energy stored by object should be larger than that if it were raised slowly to the same height. But it ...
- 571
34
votes
5
answers
65k
views
Why is the potential energy equal to the negative integral of a force?
Why is the potential energy equals to the negative integral of a force? I am really confused with this negative sign. For example, why there is a negative sign in the gravitational potential energy ...
- 736
1
vote
2
answers
269
views
How this formula for work follows from the definition?
If a particle moves along a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ then the work done by a force $\mathbf{F}$ is defined by
$$W = \int_{\gamma} \mathbf{F} = \int_{I}\mathbf{F}(\gamma(t))\...
- 36.4k
0
votes
2
answers
130
views
Mathematical misunderstanding of Work-Potential Energy Theorem?
This is a relatively basic question, but I don't understand why it is the case. This is from my dynamics book and is mainly a mathematical misunderstanding.
$$
\ dU = F\cos\theta ds
$$
Which means ...
- 101