What is Conservative force: Definition and 84 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.
Homework Statement
Suppose we have a two blocks of masses m1 and m2, one on the top of another. The lower block is attached to a spring which is attached to the wall. These two blocks are on a zero-friction floor. We give the lower block a velocity so that the upper block is not sliding on the...
Hello frnds, i understand what conservative and non conservative force are but i didn't get it properly with practical example. so any article is there which explain it properly with practical example and in easy way, i searched but didn't get any article that satisfy me.
Homework Statement
Find the potential of the following conservative and central-symmetric force
\vec{F(\vec{r})}=\vec{r}f(\vec{r})
Homework Equations
\vec{F}=-\nabla U
The Attempt at a Solution
I can integrate by components?
F_{x}=-\frac{\partial U}{\partial x}
Getting: U_{x}=-\int...
Homework Statement
A mass is placed at the top of a frictionless incline track. The bottom of the track goes into a loop. At what minimum height does the block with mass m have to be released above the ground in order to reach point b (the top of the loop).
Homework Equations...
Homework Statement
A sleeve of mass m is constrained to move without
friction along the x-axis. The sleeve is connected to the point (0, 2) on the y-axis by a spring as shown in
the diagram below. Assume that Hooke’s “Law” is a good approximation for the restoring force exerted by
the...
If the total work done is calculated using the area of the closed curve (Force vs Displacement), then the formulation doesn’t care if the force is conservative or not. Is that right? For instance, if I understand it right, spring force is a conservative force and hence work done by the spring...
Homework Statement
[PLAIN]http://img293.imageshack.us/img293/9080/omgay.jpg
Homework Equations
?
The Attempt at a Solution
?? I'm already lost at where to begin.
Conservative vector fields and line integrals
Homework Statement
A particle is subject to a force F defined by F\left( x,y \right)=\left(\begin{array}{c} y^{2} \\ 2xy \end{array}\right). The particle moves in a straight line C from (-1,2) to (1,3).[a] Calculate the work done by the force F as...
Why does work done by a conservative force = 0 in a closed path?
I know this sounds foolish :rolleyes: but how can some forces have such a property?
Can anybody give a satisfactory physical explanation?:confused:
Homework Statement
show that the force F(x,y) = (x^{2}+3y+11)\widehat{x} + (3x +5y^{3}+11)\widehat{y} is conservativeHomework Equations
it's conservative if \nabla X F = 0The Attempt at a Solution
ok, I know how to take the gradient of a function like F(x,y) = x^2 + 3xy + 3 + y, but I'm not...
Homework Statement
Find the potential functions for these conservative forces:
(1)F=xi+yj
(2)F=yi+xj
Homework Equations
F=-\nablaV (Force = -del (Pot.energy))
The Attempt at a Solution
So, I'm guessing to get V I just need to integrate F. For the first equation that gets me...
Conservative force ?
Hi all,
Work or mechanical work in physics and kinesiology, is more narrowly defined as the product of force applied over a distance. If the distance traveled is zero, than any force times zero is zero (U = F x 0 = 0).
So if I move a weight overhead 1m with the...
Homework Statement
A single conservative force F(x) acts on a 2.4 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by
U(x) = -4xe-x/4
where x is in meters. At x = 5.0 m the particle has a kinetic energy of 5.2 J. (a) What is the mechanical...
Hello all,
I understand the fact that the principles
LaTeX Code: F= \\nabla \\phi .
LaTeX Code: \\nabla \\times F = 0 .
must apply in order for a force field to be conservative however what i don't get is why showing:
LaTeX Code: f_y= g_x, f_z= h_x, g_z= h_y
where subscripts are what you...
Briefly describe a sidereal frame of reference, and then state Newton's laws of motion
I can't find sidereal in the index of my textbook, but my googling leads me to conclude that it's something to do with fixed stars. I'm not sure if a sidereal frame is also an inertial frame. Newtons laws...
Homework Statement
I read online in several places that any particle in motion in a conservative force field undergoes simple harmonic motion for small amplitudes.
I am attempting to prove this is true out of my own curiosity, but I don't know if I have the tools necessary to prove it. My math...
Homework Statement
What is the difference between two of the forces above?? Can someone please give me an example so that it's easier for me to understand
Homework Equations
The Attempt at a Solution
Homework Statement
Show that a central force between two objects, ie. one that acts along the vector connecting their centres, r^{\Downarrow},with a strength that depends on only r, is a conservative force. I am supposed to do this in cartesian coordinates and show that the work is zero or...
Hello,
I have a question about conservative forces.
'A particle is moving according to r = a cos(wt) i + b sin(wt) j, where a and b are constants, w is angular velocity, r is a vector and i,j are unit vectors that point the same direction as the x and y axes, respectively. I am asked to...
a bullet with a mass of .02kg and a velocity of 800m/s is fired horizontally into a tree. the tree exerts a resistive force and brings the bullet to rest after it penetrates .56m into the tree. given this information fins the constant resistive force exerted by the tree on the bullet and the...
friction as a nonconservative force
I was wondering, can the friction force be split up? Suppose you have a friction force working under an angle alpha, can you just say Fx = Ffric*cos(alfa), Fy = Ffric*sin(alfa)
Suppose you're working in a flat horizontal plane, and you launch a ball in 45°...
Homework Statement
For the following force, determine whether it is conservative or not.
Homework Equations
F=i(5abx^2+2ab^2y^5)+j(7abz^2+a^2b^3y)+k(18abz^3)
i, j, k being unit vectors and a and b are constants
The Attempt at a Solution
I found the curl to be...
In a given displacement of a particle, its kinetic energy increases by 25 J while its potential energy decreases by 10 J. Determine the work of the nonconservative forces acting on the particle during this displacement.
a. –15 J b. +35 J c. +15 J d. –35 J e. +55 J
workdone by...
Homework Statement
A mass m hangs on a vertical spring of spring constant k.
(a) How far will this hanging mass have stretched the spring from its relaxed length?
(b) If you now push up on the mass and lift it until the spring reaches its relaxed length, how much work will you have done...
Homework Statement
A surfer is catching a wave. Suppose she starts at the top of the wave with a speed of 1.93 m/s and moves down the wave until her speed reaches 12.3 m/s. The drop in her vertical height is 2.95 m. If her mass is 72.3 kg, how much work is done by the (non-conservative)...
how to find mathematically that a force is conservative?i know that a consrvative force is a force in which work done is independent of path followed such as gravitational force.
hello, i am having problems with this question
"If a force on an object is always directed along a line from the object to a given point, and the magnitude of the force depends only on the distance of the object from the point, the force is said to be a central force. Show that any central...
Homework Statement
If a force on an object is always directed along a line from the object to a given point, and the magnitude of the force depends only on the distance of the object from the point, the force is said to be a central force. Show that any central force is a conservative force...
My question: Show that \vec{F} is a conservative vector field then find a potential function "f" such that \vec{F} =\nabla f .
\vec{F} (x,y) = sin(y)\vec{i} + (xcos(y) + sin(y))\vec{j}
I worked the problem and found out that the force was conservative and I found the potential...
hello I am having a few troubles on these two force field problems, determining whether that are conservative or not.
F = (x, y, z) / (x^2 + y^2 + z^2)^3/2
and
F = (x, y, z) / (x^3 + y^3 + z^3)
i know that when the force is independent of the path then the force is said to be...
a single conservative force f(x) acts on a 1.0 kg particles that move along the x axis. the potential energy u(x) associated with f(x) is given by u(x)=-4xe^(-x/4) J, where x is in meters. at x=5.0 m, the particles has a kinetic energy of 2.0J. a) what is the mechanical energy of the system...
Hello everyone,
I'm a little confused on how potential energy is related to a conservative force. Say some system has potential energy U. There is a relation stating that
\vec{F} = \nabla U
I understand the F is some conservative force, but does it represent the net conservative force...