If a force of 5 pounds stretches the spring 2 inches, find K. How far will 18 pounds stretch the spring
K = 5Lbs/2In = 2.5 Lbs/In.
d = 18Lbs / 2.5Lbs/In = 7.2 In.
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To find the spring constant (K), you need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount it stretches or compresses. Mathematically, this can be represented as F = K * x, where F is the force applied, K is the spring constant, and x is the displacement.
In the given question, we are given that a force of 5 pounds stretches the spring by 2 inches. Using Hooke's Law, we can write this as 5 = K * 2. Now, we can solve for K.
Dividing both sides of the equation by 2, we get: K = 5 / 2 = 2.5 pounds per inch.
Now, to find how far a force of 18 pounds will stretch the spring, we'll use the value of K we just calculated. We can rearrange Hooke's Law as x = F / K to find the displacement.
Plugging in the given values, we have: x = 18 / 2.5 = 7.2 inches.
Therefore, a force of 18 pounds will stretch the spring by 7.2 inches.
Keep in mind that this calculation assumes that the spring follows Hooke's Law within the given force range and that the spring is linear and ideal.