What is Conservative forces: Definition and 76 Discussions
A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero.A conservative force depends only on the position of the object. If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.
Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force.
Other examples of conservative forces are: force in elastic spring, electrostatic force between two electric charges, and magnetic force between two magnetic poles. The last two forces are called central forces as they act along the line joining the centres of two charged/magnetized bodies. A central force is conservative if and only if it is spherically symmetric.
Hello Everyone,
This is not a completely new dilemma but I have been discussing it with several people and teachers and read different physics textbooks and continue to get different perspectives, sometimes overlapping sometimes not.
Let me explain and summarize:
Forces are interactions...
Goldstein writes
"only if ##V## is not an explicit function of time is the system conservative"That means ##V(r,\dot{r})## is a conservative potential, however I think that only potentials of the form ##V(r)## are conservative potentials.
Could you please tell me where I'm going wrong.
Thank you.
Hello,
I would like to review and validate some concepts that I have been recently thinking about. Hope this is correct and useful to others that need to refresh these concepts.
Forces can be classified as either conservative or nonconservative. Dissipative forces are always nonconservative...
Hello
I've written that homework statement as an example to illustrate my doubt:
How can I tell if a force is conservative or not?
I've read that, if the curl of the force is 0, it's conservative. But what about the friction force (##f=\mu N##)? Its curl is also zero, but it's not conservative...
I was referring to the conservative and non conservative forces. When i was thinking about it for example when i apply force on an object on the table the object moves a distance and when i remove the force the object does not come back to original position. Can i assume that the force i apply...
Work done by conservative forces adds potential energy (by definition of conservative force), and potential energy can only be internal to a system. Thus, conservative forces must be internal to a system.
Is this reasoning correct?
Is it confusing to find when is Work done by a force negative or positive? It indeed can be. Learn in this chapter how the dot product of force and displacement can give you the value of work done by the force and also if it is negative or positive
I actually have a few things I'm thinking about here. I'm curious as to whether a velocity dependent force field absolutely cannot be a conservative force field, in principle. I have at times come across statements in physics that I found out had mathematical exceptions for, but we don't...
Why do conservative forces conserve mechanical energy while non conservative forces do not?
According to me,
What makes the conservative forces path independent is that for a particular case they always act in a fixed direction irrespective of the direction of motion of the object on which they...
A common student misconception is that when a ball is thrown straight up in the air, at the point of maximum height, where the velocity is zero, the acceleration is also zero. This can easily be dispelled by observing that, if indeed the acceleration were zero when the velocity is zero, the...
How do conservative forces exactly conserve mechanical energy while non conservative forces do not. Also why is potential energy defined only for conservative forces?
...Or do they? I read on a book a few years ago that you can spot a conservative force seeing if it depends on the position or not. That means a non conservative force doesn't depend on the position. What is the physical reason for the relationship between a force being conservative and the...
I do not understand the reason why a conservative force always "tries" to reduce the potential energy of a system at its minimum (forgive me if I said it in a wrong way).
The explanation I gave me is: since for a conservative force, from the definition of potential energy, W=-\Delta U that...
Could anyone help me with the following questions?
- Why is the work done by conservative forces equivalent to the potential energy?
- Why is the variation of the potential energy in such cases equals to the variation of the work function?
Thanks!
I not understand because why if I have a (constant) force of friction and I apply the curl, I finding that this not is equal to zero, since this force is non conservative.
Homework Statement
Why is potential energy variation between two points equals to the work of the opposite of conservative forces between these two points?
Homework Equations
If we call these forces $$\vec F_ext^C$$
\begin{equation}
\Delta E_p=E_p(B)-E_p(A)=-\sum W_{A\rightarrow B}(\vec...
Homework Statement
Homework Equations
W=-ΔU for conservative force.
The Attempt at a Solution
Let all three forces be conservative.
Since particle comes back to where it was, ΔU=0.
Hence ΔUAB+ΔUBC+ΔUCA=0
Hence WCA=-WAB-WBC
For case A, if both WAB, WBC>0, then WCA<0. Else its greater than...
amount of work done by conservative force
=amount of decrement in potential energy
Is this correct?I think yes
Because I have been told that
Work done by non-conservative forces + work done by conservative forces = change in kinetic energy
but
Work done by non-conservative forces = change in...
When we say that conservative forces don't vary with time, we are talking about a specific position, right? Because if the position is allowed to vary with time, then the force varies with time.
In general, the (net) force on a body may be written (in one dimension) as ##F = m\ddot{x} = mv...
Homework Statement
A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion.(Figure 1) Assume that the ball travels freely in this vertical circle with negligible loss of total...
Homework Statement
A particle of mass m moves in a horizontal plane along the parabola ##y = x^2##. At t=0, it is at the point (1,1) with speed v0. Aside from the force of constraint holding it to the path, it is acted upon by the following external forces:
A radial force: ##\vec F_a = -A...
Homework Statement
A block with mass m rests on a smooth, frictionless ramp with mass M and height h. The ramp itself sits on a frictionless horizontal surface in which it is free to slide. The block slides smoothly down the ramp from rest. We want to find the speed of the block after it has...
We generally take the force of gravity to be conservative, but what if the source of gravity is moving through space? Then the force would only be conservative relative to the source, correct?
As another example, consider someone in a balloon ascending with constant speed relative to earth...
1. A single conservative force acting on a particle within a system varies as
= (− Ax + Bx6)ihat N, where A and B are constants, is in Newtons, and x is in meters.
(a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0.
(b) Find the change in...
I am following along with Goldstien's Classical Mechanics Book and I am on page 11. The text is breaking down the total potential energy of a system into two parts: the external conservative forces and the internal conservative forces. My question pertains to the internal forces.
Writing the...
A mass m = 6.2 kg hangs on the end of a massless rope L = 1.96 m long. The pendulum is held horizontal and released from rest.
1) How fast is the mass moving at the bottom of its path?
I calculated this to be 6.201 m/s using the equation v=√(2gh) (correct)
2) What is the magnitude of the...
Hi, all there are equation in the pic but I can't understand them. I know work-energy principle which
is W= F * X (work equals force times way) but I think they are special forms. What concepts
and topics should I study to understand them?
Homework Statement
Consider two identical objects released from rest high above the surface of the Earth (neglect air resistance for this question).
In Case 1 we release an object from a height above the surface of the Earth equal to 1 Earth radius, and we measure its kinetic energy just...
Can you tell me more about Non Conservative Forces? In non conservative forces like friction work done is dependent on the path that we take to reach one position to the other position but how? And why does potential energy have a meaning only for conservative force field and not...
1. The problem statement
I'm trying to show that the magnetic force is only conservative if dB/dt=0
Homework Equations
F=q[E+(v\timesB)]
Conservative if ∇\timesF=0
∇\times(A\timesB)=A(∇\cdotB)-B(∇\cdotA)+(B\cdot∇)A-(A\cdot∇)B
Maxwells equation: ∇\timesE=-∂B/∂t
The Attempt at a Solution...
I have a general understanding of what a conservative force is. I am wondering if its possible to confuse a non conservative force with a conservative one.
for example, speaking hypothetically, if you were measuring a force in an referance frame that was moving with constant acceleration...
Can work also be the transformation of energy? For instance, an object in free fall goes from an initial height (that has potential energy) to a final height where there is kinetic energy. If energy is conserved then how is work being done?
I read in a book that if the constraint forces do work, the system is conservative, else it's nonconservative. In that case, consider a system of two bodies moving in an elliptical path under gravitational attraction. Since the gravitational force is continuously doing work on the particles, by...
Homework Statement
Kibble book exercise 1, chapter 3. It is the following:
Find which of the following forces are conservative, and, for those that are conservative, determine the corresponding potential energy function (a and b are constants, and a is a constant vector)
ii) Fx= a*y...
Im SOOOO Confused.
Im studying Work, Energy and Society and I'm really darn confused.
I have the highest mark in the course, and If I'm confused, I'm wondering how others are feeling.
Whenever I have multiple questions, and they may sound stupid but please help me out:
1. Does Fg do...
1. A 750-kg automobile is moving at 20.0 m/s at a height
of 5.0 m above the bottom of a hill when it runs out of
gasoline. The car coasts down the hill and then continues
coasting up the other side until it comes to rest.
Ignoring frictional forces and air resistance, what is the
value of...
Homework Statement
(This was a problem in an examination test of physics)
Problem:
point 1) Make an example of conservative force;
point 2) Write the vectorial expression
point 3) Choose a coordinate system and find the expression of the potential energy in a generic point in the space...
I'm having trouble with the concept of conservative forces. I've been studying things of that nature for awhile now and can make most calculations on my own, but there are a few specific details that confuse me. It's easiest to explain my confusion with two simple examples.
First Example...
Homework Statement
It asks me to work out the work done by force P and it tells me that the ball m has a CONSTANT speed during its displacement.
That diagram is taken from a book which has already solved the excercise without using the concepts of energy and conservative forces. It used a...
Im kind of struggling with some conservative/nonconservative force problems. Someone please help me.
Homework Statement
A 1.8 kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.3 N is exerted on it by water resistance. Let...
I've managed to really confuse myself on the conservation of energy in a system. I guess the basic question boils down to why is the total mechanical energy of a system a meaningful quantity.
I understand E for a point particle in a conservative field is constant. I understand E for CoM...
In both voltage and gravity, I know that the work done in moving a particle between two points is independent of the path taken.
For my problem, it states "what if the path did make a difference?"
I'm suppose to design a device/machine that will move a particle or object repeatedly between...