All Questions
55
questions
2
votes
5
answers
317
views
Can a conservative force not conserve mechanical energy because of explicit time dependence?
Let us define a conservative force as being a force whose work is path independent. Then, in particular, a vanishing force is conservative.
If a force acting on a particle can be written from a scalar ...
- 17.8k
1
vote
1
answer
210
views
Meaning of "a force that derives from potential energy"
In mechanics course, when the idea of equilibrium was introduced they included the idea of a force that derives from potential energy which is the force $F$ which is related to the potential energy $...
user214810
0
votes
4
answers
390
views
Why do physicists take the convention that a force field is the negative gradient of a scalar field?
A conservative force is naturally the vector gradient of a given scalar field . I don't know why the convention to put the negative sign in front of the gradient operator.
Or is this just a ...
- 109
1
vote
1
answer
95
views
Is there any physically sound argument about why we are allowed to interpret $\dot{\vec p}$ as another force in D'Alembert's principle?
In Analytical Mechanics, when we derive the D'Alembert's principle for dynamical systems, we generally argue as;
Since $\vec F^{ext} = \dot{\vec p}$ by Newton's second law, we can interpret it as if
...
- 2,283
4
votes
1
answer
127
views
What does it mean for a force to 'produce' virtual displacement?
Book: Variational Principles of Mechanics by Lanczos, 1st edition, 1949.
Statement (page 80):
"Two systems of forces which produce the same virtual displacements are dynamically equivalent."...
- 41
1
vote
4
answers
1k
views
Sign of work done by friction
In Goldstein's classical mechanics (3rd ed.) we read:
"The independence of W12 on
the particular path implies that the work done around such a closed circuit is zero,i.e.
$$\oint \textbf{F}.d\...
- 147
0
votes
1
answer
3k
views
Calculating the work done by a particle experiencing a force in polar coordinates
Above is the source of uncertainty I have in understanding the motion of this particular particle. I'm consider (a) here, and here is my thinking:
The particle's motion is hard for me to understand. ...
- 3,200
1
vote
2
answers
167
views
Why can we not set each applied force equal to zero?
With reference to page 17 of "Classical Mechanics" by Goldstein, Safko and Poole, the small paragraph after eq. 1.43,
$$\sum_i \mathbf{F}^{(a)}_i \cdot \delta \mathbf{r}_i ~=~ 0.\tag{1.43}$$
I do not ...
- 21
2
votes
2
answers
261
views
Work done by static friction during rolling while slipping?
I'm a bit confused on whether, during slipping while still rotating, friction does work on the object. I know there are multiple questions on SE that address the rolling case, but this is very ...
- 1,177
-1
votes
4
answers
5k
views
Does a force do work if the direction of displacement is not in the direction of it (except the case of 90 degree)?
From Work (Physics) - Wikipedia:
In physics, a force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force.
According to the ...
- 5,819
2
votes
1
answer
12k
views
How to prove force is conservative?
How do I prove whether a force perpendicular to the motion is conservative and $\mathbf{F}=\mathbf{F_{0}}\sin(at)$ conservative, where $\mathbf{F_{0}}$ is a constant vector.
I knew that for a force ...
- 494
-1
votes
3
answers
10k
views
In the equation "Power=Force . Velocity", if velocity is considered constant, how can force exist?
Power(P)=Force(F) . Velocity(V)
"In the straightforward cases where a constant force moves an object at constant velocity, the power is just P = Fv. In a more general case where the velocity is not ...
- 439
1
vote
1
answer
308
views
Potential of conservative generalized forces
In Gregory's Classical Mechanics there's a proof that when a standard system is conservative, the generalized forces $Q_j$ can be written as a potential. But I can't seem to explain some steps in the ...
- 13
1
vote
0
answers
100
views
Why we can use partial derivatives to tell if a force is conservative? [duplicate]
Let us, initially, analysis only a two dimension situation. Assume that $F(x,y)$ is a force dependent on the particle position (give by $x,y$) is proposed that if
\begin{equation}
\frac{\partial \...
- 157
0
votes
1
answer
215
views
Solenoidal forces
As far as I know a solenoidal vector field is such one that
$$\vec\nabla\cdot \vec F=0.$$
However I saw a book on mechanics defining a solenoidal force as one for which the infinitesimal work ...
- 17.8k