PreCalculus
posted by Karen
The amount of force required to compress a spring is inversely proportional to the distance that it has been compressed. For one certain spring, it takes 5 pounds of force to compress it from its natural length of 18 inches down to 12 inches. How much force would be required to compress the spring down to 9 inches? Thank you. Is there a formula for this not sure how to approach it...

DonHo
F = k*deltax
F=force
k= spring constant
deltax= change in distance
find spring constant k:
5lb = k*(1218)in
k = 5lb / (1218)in
k= 0.8333 lb/in
force to compress spring to 9inches:
F = 0.8333lb/in * (918)in 
DonHo
Sorry, I didn't solve it in a calculus manner.
F= ∫kdx with upper and lower limits of distance
Integrating:
F= k*(x_f  x_i)
x_f = final distance , x_i = initial distance
and the rest should be the same as above post.
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