Question

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...
F = k*deltax

F=force
k= spring constant
deltax= change in distance

find spring constant k:

5lb = k*(12-18)in

k = 5lb / (12-18)in

k= -0.8333 lb/in

force to compress spring to 9inches:

F = -0.8333lb/in * (9-18)in


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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