And for Part 2, I understand that springs are conservative forces, but I thought that since it was some wacked spring, it might somehow change the conservative nature...could someone explain to me why it doesn't...
You just discovered a peculiar spring which follows the force law F = -Kx3. K is a constant and x = l - l0, where l is the stretched or compressed length of the spring, and l0 is the unstretched and uncompressed length of the spring.
How much work W is done on this spring when it is stretched by an amount x from its relaxed position?
ANSWER: W = Kx4/4
Which one of the following statements is correct?
(a) The force of this unusual spring is a conservative force.
(b) The force of this unusual spring is a non-conservative force.
(c) Not enough information is given to determine whether the force is conservative or non-conservative.New and unusual spring?
It has to do with energy. The spring stores energy, which makes the force conservative. There is no energy lost outside the system, is the other test to tell if conservation applies.
The previous answerer noted that the W is the integral of the Force. That is true in all cases where forces are conservative. F*d, for a constant force is the integral of a constant over a displacement. F is function of x. For a spring that has force k*x, this is a function and the integral is .5*k*x^2. You will learn that as long as the force has a functional relationship to the displacement, it is conservative. When I state functional, it must meet the mathematical tests of a function. With calculus, which Sir Issac Newton invented to explore physics, you will be able to manipulate the force energy relationship on more complex forces.
In the first part of this problem we have
F=K*x^3
the definite integral from 0 to x is work over that displacement
W=K*x^4/4
__________________-New and unusual spring?
The integral from 0 to x of ( Kt^3 ) is Kx^4/4
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