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alphabeta1720
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Is there any way to prove that a given force is conservative?
alphabeta1720 said:Is there any way to prove that a given force is conservative?
Yes, there is. The work done in moving an object using that force along a path in the plane by [itex]\int_p \vec{F}\cdot d\vec{s}= \int_p f(x,y)dx+ g(x,y) dy[/itex] depends only on the beging and ending points and is independent of the specific path. Once can show that that is true if and only if there exist some "potential function" G(x,y) (numerical valued, not vector valued) such that [itex]\nabla G= \vec{F}[/itex] which just means thatalphabeta1720 said:Thank you for that
but can anyone help me solving these problems (Sorry, but I don't know about 'curl' and 'del' operators)
Q1 Consider the two dimensional force F = f(x,y) i + g(x,y) j . Is it possible to determine whether this is a conservative force without any additional information? What if f(x,y) = f(x)
and g(x,y) = g(y)
Apply the conditionQ2 which of the following forces is conservative?
A) F = y i - x j B) F = xy i - xy j
C) F = y i + x j D) F = xy i + xy j
E) F = 3x i + 4y j
(There may be more than 2 correct answers)
Thank You
HallsofIvy said:(I can't help but think that if you are asked a question like this, you are expected to have learned all this before!)
A conservative force is a force that conserves mechanical energy. This means that the work done by the force is independent of the path taken by the object. In other words, the work done by a conservative force only depends on the initial and final positions of the object, not on how the object got from one position to the other.
One way to prove that a force is conservative is to show that the work done by the force along a closed loop is zero. This means that the object returns to its initial position and has the same amount of energy as it did before. If the work done by the force is not zero, then the force is not conservative.
No, a non-conservative force cannot become conservative. A force is either conservative or non-conservative and cannot change its nature. For example, friction is a non-conservative force and will always dissipate energy, it cannot suddenly become a conservative force.
No, not all fundamental forces in nature are considered conservative. The four fundamental forces are gravity, electromagnetism, weak nuclear force, and strong nuclear force. Of these, only gravity and electromagnetism are considered conservative forces.
Conservative forces are closely related to the concept of potential energy. A conservative force can be defined as the negative gradient of a potential energy function. This means that the work done by the force can be calculated by taking the difference in potential energy between the initial and final positions of an object. In other words, conservative forces can store potential energy, which can be converted into kinetic energy as the object moves.