If a force of 5 pounds stretches the spring 2 inches, Find K. How much force is necessary to stretch the spring 14 inches
K = 5Lbs / 2 In. = 2.5 Lbs/In.
F = 2.5Lbs/In * 14In. = 35 Lbs.
and
To find the value of the spring constant (K), we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law equation: F = -K * x
Where:
F is the force applied to the spring,
K is the spring constant, and
x is the displacement of the spring from its equilibrium position.
In the given scenario, we have a force of 5 pounds stretching the spring 2 inches. Plugging these values into the formula, we get:
5 = -K * 2
To solve for K, divide both sides of the equation by -2:
5 / -2 = K
K = -2.5 pounds/inch
Now, to find how much force is necessary to stretch the spring by 14 inches, we can use Hooke's Law again:
F = -K * x
Plugging in the new displacement value of 14 inches, we have:
F = -(-2.5 pounds/inch) * 14 inches
Simplifying this expression:
F = 2.5 pounds/inch * 14 inches
F = 35 pounds
Therefore, a force of 35 pounds is necessary to stretch the spring by 14 inches.