All Questions
55
questions
-4
votes
1
answer
97
views
Does every object have an infinite amount of energy? [duplicate]
If energy is defined as the capacity to do work, and the formula for work is force times displacement, if we place an object on a frictionless surface and apply any amount of force to said object, the ...
0
votes
2
answers
74
views
Why is the work done by moving an object up vertically not greater than mgh
Watching Walter Lewin's classical mechanics. In lecture 11 he says when moving object up vertically distance h, the work done by gravity is -mgh, which makes sense. But then he said the work done by ...
-1
votes
1
answer
63
views
Conservative forces and Variation
I am currently studying "Classical mechanics by Goldstein" and have just started. The book introduced something simple. For a conservative force, the work done in taking a mass from one ...
- 585
0
votes
1
answer
40
views
Getting different answers by different methods for angle made by a pendulum moving with constant acceleration
A point mass $m$ is hanging by a string of length $l$ in a car moving with a constant acceleration $a$. Using car frame and pseudo force, we easily get that the angle made by string with vertical is :
...
- 341
1
vote
1
answer
56
views
Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]
John Taylor's Classical Mechanics says this...
I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the ...
- 97
1
vote
2
answers
98
views
Why is force "accumulated" more at a higher speed?
I tried to understand why kinetic energy is proportional to the square of velocity. In this endeavor I stumbled upon a book "Emilie du Chatelet: Daring Genius of the Enlightenment" (ISBN 978-...
- 112
1
vote
2
answers
108
views
Law of Conservation of Energy ambiguity in Giancoli textbook
In my version of the textbook by Giancoli: Physics for Scientists and Engineers, in chapter 8, there is a formulation of the law of conservation of energy that seems unintuitive and correctable to me. ...
0
votes
1
answer
46
views
Why is the force being the differential of a potential equivalent to it being a conservative force?
I was reading Goldstein's book on mechanics and came across this theorem:
$F(r) = - \nabla V(r)$ is a necessary and sufficient condition of the force field being conservative.
So far, I have ...
- 169
1
vote
1
answer
98
views
Can Lagrange's equation be used if the virtual work done by constraint forces is not zero?
I'm learning analytical mechanics and was just introduced to d’Alembert’s principle, which I know is only valid when constraint forces' virtual work is zero. My question is, does this restriction also ...
- 468
1
vote
1
answer
90
views
Work done in sliding a block across a table, as seen in different inertial frames
Suppose, I'm pushing a block across a smooth table.
The length of the table is $d$, and the force that I applied is $F$.
According to an observer at rest, standing next to the table, the work done is $...
- 493
0
votes
2
answers
75
views
Is the value of the work done by the forces acting on a rigid body frame dependent?
I was going through the definition of "Work of Forces Acting on a Rigid Body" in Wikipedia .
Here they have mentioned that work done can be calculated by taking any reference point on the ...
- 1,568
0
votes
1
answer
258
views
Is impulse functionally equivalent to work and therefore expressible in Joules?
I am trying to understand things at at a fundamental and conceptual level.
Givens...
1 kg mass
Mass is at rest (relatively, of course)
Mass is on an idealized frictionless surface
1 N of force is ...
- 161
0
votes
3
answers
96
views
Why the weight vector is perpendicular to the displacement of the object being moved by the tension force in the conical pendulum?
Can someone explain why, in the conical pendulum, the weight vector is perpendicular to the displacement of the object being moved by the tension force in the system? I understand that the tension ...
user282164
20
votes
3
answers
4k
views
Conditions for a force to be conservative
Taylor's classical mechanics ,chapter 4, states:
A force is conservative,if and only if it satisfies two conditions:
$\vec{F}$ is a function of only the position. i.e $\vec{F}=\vec{F}(\vec{r})$.
The ...
- 1,295
0
votes
1
answer
138
views
Simple Force/Work Problem
In "Thinking Physics" there is a question about pushing a barrel up a ramp. The barrel is 100 pounds and the ramp is 3 feet high and 6 feet on the hypotenuse. The question is how much force ...
- 749
0
votes
2
answers
153
views
Does work increases as accelaration increases?
If work is a product of force and displacement, and force increases as acceleration increases, does these mean that work is dependent on acceleration? For instance, if I lift a block faster, does this ...
5
votes
4
answers
2k
views
Work done by constraint forces -- Generalisation
Consider the above scenario: In the subsequent motion, we need to find the work done by tension on the (trolley + mass) system.
Solution: Suppose at an instant, the velocity of the trolley (and hence ...
- 1,295
0
votes
1
answer
133
views
The "coefficients" of virtual displacement in Goldstein's classical mechanics
In Goldstein's classical mechanics the following passage is confusing me:
We therefore have as the condition for equilibrium of a system that the virtual work of the applied forces vanishes: $$\sum_i ...
- 6,963
0
votes
2
answers
459
views
Path independence of a conservative force
My book Halliday et al. gives a proof of the path independence (conservative force). It is said that the net work to move a particle from a to b and then from b to a is zero. Thus the work done from a ...
user248666
2
votes
3
answers
720
views
Work done by tension on a system-generalisation
In All the Classical Mechanics problems I have come across so far, There's one thing that happens invariably: That the work done by tension is zero. Mostly, It simply happens because the (massless) ...
- 1,295
0
votes
2
answers
615
views
Work done by friction over closed path
I am stuck thinking about work done by non-conservative forces. It is path dependent.
Let us consider an example.
A truck starts from rest and a block is kept on it. It accelerates for some time and ...
- 125
2
votes
1
answer
143
views
Example of a single constraint force doing virtual work despite the sum of work done by constraints being zero
When deriving d'Alembert's Principle it must be assumed, that the total virtual work done by constraint forces vanishes.
$$\sum_{j=1}^N\mathbf{C}_j\cdot\delta \mathbf{r}_j=0.$$
In the books I've read, ...
- 72
1
vote
2
answers
144
views
Work done as change of potential, how total derivative is converted to partial derivative
I am reading Goldsetein's Classic Mechanics 3rd edition in Chapter 1 it says,
If work done in moving form point 1 to 2 denoted by $W_{12}$, is independent of the path it should be possible to ...
- 113
0
votes
2
answers
192
views
In order for a force to be derived from the gradient of a potential energy, does the work done by such a force need to be invariant of the path?
Suppose a force $\mathbf{F} = \mathbf{F}(\mathbf{r}, t)$ where $\mathbf{r}$ is a three dimensional space vector and $t$ is time.
I understand that in order to a force be conservative two conditions ...
- 376
0
votes
1
answer
104
views
Equation for total work for a system of particles, modeled as a single particle, acted upon by multiple variable forces in three dimensions?
I am attempting to generalize the equation for the total work done by multiple, constant forces on a system that can be modeled as a single particle (that is, a system that moves so that all the parts ...
- 125
3
votes
4
answers
2k
views
Why the total virtual work done by forces from constraints vanishes? (Perpendicularity of two or more particles)
My mechanics book claims that the total force on the $i$-th particle is
$$
F_i=K_i+Z_i \tag{2.5}
$$where $Z_i$ is the force due to constraints and $K_i$ the real, dynamic force. Then, the book states ...
- 1,335
2
votes
1
answer
2k
views
Is total mechanical energy always equal to maximum potential energy?
Am I correct in stating this: When initial velocity of an object is $0$ then the total mechanical energy will always be equal to the maximum potential energy (with maximum height or displacement) (...
- 23
1
vote
2
answers
10k
views
Work done by a person climbing stairs, who or what does the work? [duplicate]
I've seen other questions like this but didn't really see any answers.
When a person climbs stairs, the object is the person. Yet we say the person did work...how so? Doesn't work mean an external ...
- 379
3
votes
1
answer
358
views
Conservative field vs conservative force
For a conservative field (e.g. electrostatic field) the circulation of the field (along a closed line) is zero.
For a conservative force (e.g. macroscopic elastic force) the work performed on a ...
- 719
0
votes
1
answer
125
views
Force Applied but No Distance Travelled
Suppose I push on a wall with a constant force of 5 N for 10 s. The wall won't move and hence no work will be done on the wall. However, pushing requires energy. How can I find out how much energy I ...
- 251
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
1
vote
3
answers
9k
views
Why can't we define a potential energy for a non-conservative force? [closed]
We could define potential energies for non-conservative forces too and then we could conserve it with kinetic and potential energy as we know it. But no one does that. Why is this? Please explain. Any ...
- 913
2
votes
3
answers
16k
views
Why is walking up stairs harder than walking normally?
I must admit, I'm pretty new to studying physics and I know this is a simple concept but I'm having difficulty understanding it. I've tried reading the questions here but I just need a little bit of ...
- 123
0
votes
1
answer
296
views
Normal force, work and conservativity
I have searched very much on line, both in this site and elsewhere, but found no proof of whether the normal force is conservative or is not, in general.
Clearly, if the force is orthogonal to the ...
0
votes
1
answer
140
views
Given an initial push, is work done on an object infinite in a hypothetical empty universe?
Consider a hypothetical empty universe containing a single object. Given an initial push, will the work done by the forever moving object be infinite?
- 500
0
votes
1
answer
174
views
Gravitational work
As far as I know gravitational work is independent from the path of the object, and I have an object that goes up on a inclined plane to a certain height, and than, after the object reaches the edge ...
- 11