Question

the spring stretched from 11 cm to 35cm when a force 4N is applied.if it obeys hooke's law . what is the total length when a force of 6N is applied

Answer 1

Answer:

The force exerted by a spring is given by F = kx where k is the spring constant and x is the extension of the spring from its natural length, call it L. So we can write

4 = k(a-L)

5 = k(b-L)

Solve these equations simultaneously to find k and L in terms of a and b:

4/(a-L) = 5/(b-L)

4b-4L = 5a-5L

L = 5a-4b

First equation then gives

k = 4/(a-5a+4b) = 4/(4b-4a)

k = 1/(b-a)

Now use F = kx with F = 9, let's call the new length c.

9 = k(c-L)

9 = (c-5a+4b)/(b-a)

9b-9a = c-5a+4b

c = 5b-4a