Final answer:
The force exerted by the spring on the mass in equilibrium equals the weighing force of the mass, which is 16 pounds.
Step-by-step explanation:
The force exerted by the spring on a mass can be found by using Hooke's Law, which states that the force F exerted by a spring is equal to the negative product of the spring constant k and the displacement x from its equilibrium position (F = -kx). In the scenario where a mass weighing 16 pounds is attached to a spring with a spring constant of 36 lb/ft, we assume that the spring stretches until it reaches a new equilibrium where the force of the spring equals the weighing force of the mass. To find the force exerted by the spring, we need to convert the weight of the mass to mass units, calculate the displacement using the gravitational acceleration (32.2 ft/s2), and then use Hooke's Law.
However, if the 16-pound mass is simply hanging at rest and the system is in equilibrium, the spring exerts an upward force equal to the weighing force of the mass to balance the downward gravitational force. Since the weight of the mass (16 lb) is directly provided, and we're looking for the force the spring exerts, it equals the weight of the mass: 16 pounds.