Hooke's law. the distance d when a spring is stretched by a hanging objective varies directly as the weight w of the object. if the distance is 38 cm when the weight is 3 kg, what is the distance when the weight is 7 kg?

Hooke's law is F=-kx, which means the elastic force contained by the spring is a product of the distance it stretches and its spring constant, but the direction of the force is opposite that of the displacement. We calculate as follows:

(3 kg)(9.8 m/s^2) = -k(-0.38 m)
k = 77.4

Then use k to find the new displacement, again using Hooke's law:
(7 kg)(9.8 m/s^2) = -(77.4)x
x = -0.89 m