Hooke's Law states that the distance a spring stretches is directly proportional to the weight attached to the spring. If a 30-pound weight attached to the spring stretches the spring 8 inches, find how much weight is needed to stretch the spring 12 inches.
30=k*8
k=30/8
W=kx=30/8 * 12=...
45
To solve this problem using Hooke's Law, we can set up a proportion to find the weight needed to stretch the spring 12 inches.
According to Hooke's Law, the distance stretched (x) is directly proportional to the weight applied (y).
We are given that when a 30-pound weight is attached to the spring, it stretches 8 inches. We can represent this using the proportion:
x1 / y1 = x2 / y2
where x1 = 8 inches (original stretch), y1 = 30 pounds (original weight), x2 = 12 inches (new stretch), and y2 is unknown (new weight).
Substituting the values:
8 / 30 = 12 / y2
Now, we can solve for y2 (the weight needed to stretch the spring 12 inches):
8y2 = 30 * 12
8y2 = 360
y2 = 360 / 8
y2 = 45 pounds
Therefore, to stretch the spring 12 inches, a weight of 45 pounds is needed.
To find how much weight is needed to stretch the spring 12 inches, we can use Hooke's Law and set up a proportion.
According to Hooke's Law, the distance a spring stretches is directly proportional to the weight attached to the spring. This can be represented by the formula:
F = k * x
Where:
F is the force (weight) applied to the spring
k is the spring constant
x is the distance the spring stretches
In this case, we have the following information:
Force (weight) applied to the spring (F1) = 30 pounds
Distance the spring stretches (x1) = 8 inches
Distance we want to find the weight for (x2) = 12 inches
To set up the proportion, we can express it as:
F1 / x1 = F2 / x2
Substituting the given values:
30 / 8 = F2 / 12
To solve for F2, we multiply both sides of the equation by 12:
12 * (30 / 8) = F2
Now, let's calculate the value of F2:
F2 = 12 * (30 / 8)
F2 = 45
Therefore, the weight needed to stretch the spring 12 inches is 45 pounds.