Determining Weight Displacement with a Roller and Spring

What is the distance to which the 10lb weight is located when it is in equilibrium?

Forces Acting on the Weight

When the 10lb weight is in equilibrium, it is supported by cord AC, which exerts an upward force equal to the weight of the object. Additionally, the spring provides an opposing force due to its stiffness. At equilibrium, these two forces cancel each other out.

Determination of Weight Displacement

To determine the distance to which the weight is located when it is in equilibrium, we can use Hooke's Law, which states: F = k * x, where F is the force, k is the stiffness constant, and x is the displacement from the equilibrium position. Since the force due to the spring is equal to the weight of the object in this case, we have: 10lbs = 10lbs/in * x. By solving for x, we find that x = 1 inch. Therefore, the weight is located 1 inch from the equilibrium position when it is in equilibrium.

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