Answer:
3/8
Step-by-step explanation:
Given that:
Work required to stretch a string:
3 ft = 6ft - lb
The work required to stretch it 9 inches
Given that :
Work(W) = kx
Take the integral of W at 3 fts beyond its natural length;
W = ∫kx dx at 0 to 3
W = k ∫xdx at 0 to 3
W = 6
W = k[x²/2] at x =0 to x = 3
6 = k[3² /2] - 0
6 = k[9/2]
12 = 9k
k = 12/9 = 4/3 = 1.333
Converting inches to feet:
1 inch 0.0833 ft
9 inches = 0.75 ft
W = ∫kx dx at 0.75 to 0
W = 4/3 ∫xdx at 0 to 0.75 = 3/4
W = 4/3[x²/2] at x =0.75 to 0
W = 4/3[(3/4)²/2] at 0.75 to 0
W = 4/3[(9/16) / 2]
W = 4/3 * (9/16 * 1/2)
W = 36/96
W = 6/16 = 3/8 ft - lbs
