Question

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?

Answer 1

d=wk
38=3k
k=38/3
d=7(38/3)
d=88.666

Answer 2

The question gives you distance (0.38 m) and mass (not weight, 3 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...

Anyways, first find the spring constant using Hooke's law: (use a negative for displacement since you're going down)
(3 kg)(9.8 m/s^2) = -k(-0.38 m) --> k = 77.4

Then use that 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 which means 89 cm down.

That makes sense - you would think an object with greater mass would stretch the spring further.

Answer 3

thanx u guys!!