Final answer:
The work done to stretch the spring from x=0 to x1=39cm is 104.65J. Therefore, none of the options A, B, C, or D is correct.
Step-by-step explanation:
To calculate the work done to stretch the spring from x=0 to x1=39cm, we need to find the area under the force-extension curve.
The work done by a spring force is given by the formula: W = area under the curve = ∫Fdx
Where
F is the force
dx is the displacement.
First, we calculate the work done from x=0 to x2=67cm using the formula: W = ∫Fdx = ∫115Ndx = 115∫dx.
Since the force is constant and the displacement from x=0 to x2=67cm is 67cm-0cm = 67cm = 0.67m, the work done in this segment is: W = 115N * 0.67m = 77.05J.
Next, we calculate the work done from x2=67cm to x3=91cm. The force in this segment is constant at F3 = 115N.
The displacement is 91cm-67cm = 24cm = 0.24m.
Therefore, the work done in this segment is: W = F3 * dx = 115N * 0.24m = 27.6J.
To find the total work done from x=0 to x1=39cm, we add the work done in each segment: Total work = Work from x=0 to x2 + Work from x2 to x3 = 77.05J + 27.6J = 104.65J.
Rounded to the nearest whole number, the work necessary to stretch the spring from x=0 to x1=39cm is 105J, which is not among the given answer choices.
Therefore, none of the options A, B, C, or D is correct.