It requires 8 inch pounds of work to stretch a certain spring 2 inches from its rest position. Assuming that the spring follows hooke's law, what is k?
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To find the value of k, which represents the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, it can be represented as F = -kx, where F is the force exerted by the spring, x is the displacement from the equilibrium position, and k is the spring constant.
In this case, we are given that it requires 8 inch-pounds (in-lb) of work to stretch the spring by 2 inches. To find k, we can manipulate Hooke's Law as follows:
F = -kx
Work = Force × Displacement
Since the work is given in inch-pounds and the displacement is given in inches, we need to convert the work to force using the relationship: 1 inch-pound = force x inch.
Therefore, the work done to stretch the spring by 2 inches is: 8 inch-pounds = F × 2 inches.
Rearranging the equation, we have:
F = 8 inch-pounds / 2 inches = 4 pounds.
Now, we can substitute the force value (F) into Hooke's Law equation to solve for k:
4 pounds = -k × 2 inches
Dividing both sides of the equation by 2 inches, we get:
k = -4 pounds / 2 inches
Finally, simplifying the expression, we find:
k = -2 pounds/inch.
Thus, the spring constant (k) in this case is -2 pounds/inch.