if the work required to stretch a spring 1 ft beyond its natural length is 12 ft-b, how much work is needed to stretch 9 inches beyond its natural length?
To solve this problem, we need to use the principle of Hooke's Law. Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.
We are given that the work required to stretch the spring 1 ft beyond its natural length is 12 ft-b. From this information, we can establish a proportion between the displacement and the work done:
(Displacement 1 ft) / (Work done 12 ft-b) = (Displacement 9 in) / (Work done ?)
Now, let's convert the displacement 9 inches to feet:
9 inches = 9/12 ft = 3/4 ft
We can substitute this value into the proportion:
1 ft / 12 ft-b = (3/4) ft / Work done ?
To find the work done, we can rearrange the proportion:
Work done ? = (3/4) ft * (12 ft-b) / 1 ft
Simplifying this expression:
Work done ? = (3/4) ft * (12 ft-b)
By multiplying these values, we find the amount of work required to stretch the spring 9 inches beyond its natural length.