Hooker'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 39cm when the weight is 3kg, what is the distance when the weight is 9kg?
Thank you, before hand.
39/3 = 13 cm/kg, the spring "rate" of the spring.
Therefore, the d for 9kg is
d = 13cm/kg x 9kg = 117cm.
To solve this problem, we can use Hooker's Law, which states that the distance (d) a spring is stretched is directly proportional to the weight (w) of the object attached to it. Mathematically, we can represent this relationship as:
d ∝ w
This equation tells us that as the weight of the object increases, the distance the spring stretches will also increase proportionally.
To find the specific equation relating distance and weight, we need to introduce a constant of proportionality. Let's call this constant "k." So, we can rewrite the equation as:
d = k * w
Now, we can use the given information to determine the value of k. We are told that when the weight (w) is 3kg, the distance (d) is 39cm. Substituting these values into our equation, we get:
39 = k * 3
To find the value of k, divide both sides of the equation by 3:
39/3 = k
13 = k
Now that we have the value of k, we can use it to find the distance (d) when the weight (w) is 9kg. Substituting these values into our equation, we get:
d = 13 * 9
d = 117 cm
Therefore, when the weight is 9kg, the distance the spring stretches is 117cm.