Final answer:
To find the work done in raising one end of a 16 ft chain weighing 110 lbs to a height of 3 ft, you calculate the average force over the distance lifted. Converting units and using the formula for work, the total work required is approximately 223.6 joules.
Step-by-step explanation:
The question asks how much work is required to raise one end of a 16 ft long chain that weighs 110 lbs to a height of 3 ft. To solve this problem, we have to consider that the chain is being lifted uniformly. This means that at any given point, the height of the subsequent sections of the chain will vary linearly from 0 to 3 ft.
To calculate the work done, we use the concept of work as the product of force and distance. The force is due to the weight of the chain, and the distance is the height to which it is raised.
The average height to which the chain is raised is 1.5 ft (since it's uniform and linear from 0 to 3 ft). The weight of the chain is the force due to gravity, which is 110 lbs. Converting feet to meters (1 ft = 0.3048 m) for consistency in units and considering g = 9.8 m/s² as the acceleration due to gravity, we can calculate the work done:
First, convert the weight from pounds to newtons: 110 lbs = 489.07 N (1 lb = 4.44822 N).
Calculate the work done: Work (W) = force (F) × average height (h) = 489.07 N × 1.5 ft × 0.3048 m/ft = 223.6 J.
Therefore, the work required to raise one end of the chain to a height of 3 ft is approximately 223.6 joules.