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 23 cm when the weight is 3 kg, what is the distance when the weight is 5 kg? I need the answer badly and I do not understand the problem.

Answer 1

distance d is directly proportional to weight w
so, d = k * w (where k is some constant you don't know yet)

Answer 2

when d = 23, w = 3
so, 23 = k * 3
which means k = 23/3

Answer 3

now, you have to find d when w = 5
d = k * w
= 23/3 * 5

Answer 4

another way of thinking about it:
3 kg stretches the spring by 23 cm
so 5 kg will stretch it even more

Answer 5

3 kg stretches it by 23 cm
in other words, each kg stretches it by 23/3 cm
so, 5 kg will stretch it 5 times that much = 5 * 23/3

Answer 6

ok thanks