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 64cm when the weight is 3kg, what is the distance when the wight is 9kg?

To solve this problem, we can use Hooke's Law which states that the distance (d) is directly proportional to the weight (w) of the object.

Step 1: Set up the proportion:
We can write the proportion as:
d1 / w1 = d2 / w2
where d1 = distance when weight is 3kg (64cm), w1 = weight when distance is 3kg (3kg), d2 = distance we want to find, and w2 = weight when distance is d2 (9kg).

Step 2: Substitute the given values:
Using the given values, we can substitute them into the proportion:
64cm / 3kg = d2 / 9kg

Step 3: Solve for d2:
To solve for d2, we cross-multiply and solve the equation:
64cm * 9kg = 3kg * d2
576cm * kg = 3kg * d2

Step 4: Simplify the equation:
We can cancel out the kg units on both sides of the equation:
576cm = 3d2

Step 5: Solve for d2:
To solve for d2, divide both sides of the equation by 3:
d2 = 576cm / 3

Step 6: Calculate the value of d2:
Dividing 576cm by 3, we get:
d2 = 192cm

Therefore, when the weight is 9kg, the distance is 192cm.

To solve this problem, we can use Hooke's Law, which states that the distance a spring is stretched or compressed varies directly with the force or weight applied to it. Hooke's Law can be represented as:

d = k * w

Where:
- d is the distance the spring is stretched
- w is the weight or force applied to the spring
- k is the spring constant or proportionality constant

Given that the distance is 64cm when the weight is 3kg, we can plug these values into the equation to find the value of k:

64 = k * 3

To find k, divide both sides of the equation by 3:

k = 64 / 3

Now we can use the value of k to find the distance when the weight is 9kg:

d = k * w
d = (64 / 3) * 9
d = 192 / 3
d = 64 cm

Therefore, the distance when the weight is 9kg is also 64cm.

W=kd

Use the first set of data to find k, k=W/d

Then, use that k to find the second distance...

distance= k * w

I know you are in a math class, and the teacher probably doesn't know, but kg is not a unit of weight, but of mass. Mass only has weight under the influence of gravity, and varies with location and altitude.

CORRECT ANSWER: 189