(25 pts.) The canonical example of a variable force is Hooke\'s Law. Hooke\'s La
ID: 1788439 • Letter: #
Question
(25 pts.) The canonical example of a variable force is Hooke's Law. Hooke's Law describes the force exerted by a spring when it is stretched or compressed. The magnitude of the force is given by F, kx, where F is the force, x is the displacement of the spring from equilibrium, and k is the spring constant, which describes the stiffness of the spring. The direction of the force is opposite to the displacement x The work done by a variable force is given by: WF.ds Be sure to note the presence of the dot product between the force F and the differential displacement ds. (10 pts.) Solve the integral to calculate the work done by a spring that follows Hooke's Law when stretching from an initial position x to a final position x. a.
Explanation / Answer
1] work = integral F.dx cos alpha where alpha = 180 degree,
= integral kx dx cos 180 degree
= - kx^2/2
applying limits, work = 0.5 kxi^2 - 0.5 k xf^2
b] work = 0.5*4*[(-6)^2 - 0] = 72 J
c] work done = -[Uf-Ui]
= - [ 0.5 kxf^2 - 0.5 k xi^2]
= - [ 0.5*4*0^2 - 0.5 *4*(-6)^2]
= 72 J
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