Hooke.s Law. The distance d when a spring is streched by a hanging object varies directly as the weight w of the object. If the distance is 66 cm when the weight is 3 Kg., what is the distance when the weight is 7 Kg.
assuming all you need is confirmation the answer you obtained through your hard work,
d=154
To solve this problem, we can use Hooke's Law, which states that the distance stretched by a spring is directly proportional to the force applied to it. In this case, the force applied to the spring is the weight of the hanging object.
Let's determine the constant of proportionality first.
Given that the distance (d) is 66 cm when the weight (w) is 3 Kg., we can set up a proportion:
d/w = k (where k is the constant of proportionality)
Plugging in the values, we get:
66 cm / 3 Kg = k
Simplifying, we find:
k = 22 cm/Kg
Now that we have the constant of proportionality, we can use it to find the distance when the weight is 7 Kg.
d = kw (where w is the weight of the object)
Plugging in the values, we get:
d = (22 cm/Kg) * 7 Kg
Simplifying, we find:
d = 154 cm
Therefore, when the weight is 7 Kg, the distance stretched by the spring will be 154 cm.