Is the spring force a conservative or a non-c | vedclass

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Question

(A) The spring force is given by Hooke's Law,$F = -kx$,where $k$ is the spring constant and $x$ is the displacement from the equilibrium position.$A$

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Conservative force

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(A) The spring force is given by Hooke's Law,$F = -kx$,where $k$ is the spring constant and $x$ is the displacement from the equilibrium position.$A$ force is defined as conservative if the work done by the force in moving a particle between two points is independent of the path taken.For a spring force,the work done in moving from position $x_1$ to $x_2$ is $W = \int_{x_1}^{x_2} (-kx) dx = -\frac{1}{2}k(x_2^2 - x_1^2)$.Since the work done depends only on the initial and final positions ($x_1$ and $x_2$) and not on the path taken,the spring force is a conservative force.

Is the spring force a conservative or a non-conservative force?

Similar Questions

For a system of conservative forces,the potential energy $U$ is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. Determine the force $F$.

The graph of potential energy $U(x)$ versus distance $x$ is shown in the following figure. The force $F$ versus distance $x$ graph will be represented by (assume that the force is conservative):

Is the work done by non-conservative forces always negative? Discuss.

Assertion $(A) :-$ If work done by the force depends on the path,then the force is said to be non-conservative.
Reason $(R) :-$ All conservative forces are central forces.

The potential energy of a system increases if work is done

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