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?

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. )

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

To find the length of the spring with no weight attached, we can use the concept of proportionality. We know that the weight held by the spring is directly proportional to the length of the spring.

Let's consider the first scenario where a 2-lb weight stretches the spring to 15 inches. We can write this as:

2 lb --> 15 in.

Next, consider the second scenario where a 12-lb weight stretches the same spring to 20 inches. We can write this as:

12 lb --> 20 in.

To find the length of the spring with no weight attached, we can set up a proportion using these two scenarios. The proportion can be written as:

2 lb / 15 in. = 12 lb / x

Where 'x' represents the length of the spring with no weight attached.

We can cross multiply to solve for 'x':

2 lb * x = 15 in. * 12 lb

Now, let's solve the equation:

2x = 180

Dividing both sides of the equation by 2:

x = 90

Therefore, the length of the spring with no weight attached is 90 inches.