type as an integer or decimal rounded to three decimal points as needed

Question

Hooke's Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 30 cm when the weight is 3 ​kg, what is the distance when the weight is 8 ​kg?

the distance is ____________

Answer 1

You are given that "distance d . . . varies directly as the weight w" which means d = kw ("d" again is distance, "k" is the constant of proportionality, and "w" again is weight)

So if d = kw then k = d/w

And we know that for d = 30, w = 3 (note that this is really mass and not weight but it will work just the same since weight and mass are proportional), so we can plug those in to solve for "k":

k = d/w

k = 30/3 = 10

Therefore d = 10w

So when w = 10, d = 10(8) = 80 meaning that when the mass is 8 kg, the distance is 80 cm

Answer 2

spring force = weight of the object

k x = m g

x is proportional to m.

3 kg, 30 cm. 8 kg, 80 cm.