Question

When a spring is subjected to 4N force its length is a metre and if 5N is applied length is b metre. If 9N is applied its length is :

Answer 1

9N = 5N+4N

 LENGTH = a+b

    9N = (a+b)metres

Answer 2

Answer:

5b-4a

Explanation:

The force exerted by a spring is given by F = kx

Where K is the spring constant  and x is the elongation in the spring from its natural length, L. Thus,

= 4 = k(a-L)

= 5 = k(b-L)

Solving both the equations -

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

= 4b-4L = 5a-5L

= L = 5a-4b

Thus,

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

k = 1/(b-a)

Using F = kx with F = 9, where let the new length be = d.

9 = k(d-L)

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

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

d = 5b-4a.

Thus, if 9N is applied the length will be 5b-4a.