Question

as the weight held by a spring increases, the length of the spring increase proportionally. suppose a 2-lb weight stretches a spring to 15 in., and a 12-lb weight stretches the same spring to 20 in. what is the length of the spring with no weight attached?

Answer 1

If my sometimes "failing" memory serves me right, this is called Hooke's Law.

and L = k w + c, where L is the length and w is the weight , and c is a constant

when w=2, L = 15
when w=12 L = 20

treat it as if you had 2 different ordered pairs
(2,15) and (12, 20)
slope = (20-15)/(12-2) = 5/10 = 1/2
so L = (1/2)w + c
plug in (2,15) ...
15 = (1/2)(2) + c
14 = c
-----> L = (1/2)w + 14
so when no weight is attached, w = 0
and L = 14

(Of course this equation would make only sense within the domain of 14 and the length of the string with full extension.
I also suspect that as L approaches its maximum length, the function is no longer linear.
Physics experts can probably shed more light on this. )

Answer 2

The amount a spring stretches is proportional to the weight hung on the spring. A weight of 5Kg stretches the spring by 60cm
a. How much does a weight of 10 Kg stretch the spring?
b. What weight makes the spring stretch 24cm