Answer:
To find the work required to wind up the entire chain, we can break down the problem into steps:
1. Calculate the total weight of the chain:
Since the chain weighs 2 pounds per foot and is 24 feet long, the total weight of the chain can be found by multiplying the weight per foot by the length of the chain:
Total weight = 2 lbs/ft * 24 ft = 48 lbs
2. Calculate the distance the winch needs to lift the chain:
The winch needs to lift the entire 24-foot chain, so the distance it needs to lift is the same as the length of the chain:
Distance lifted = 24 ft
3. Calculate the work required to lift the chain:
The work done in lifting an object is given by the formula:
Work= Force x Distance
Work= 48 lbs x 24ft
Work= 1152 ft-lbs
In this case, the force required to lift the chain is equal to its weight, which is 48 lbs. Therefore, the work required to wind up the entire chain is:
So, the work required to wind up the entire 24-foot chain weighing 2 pounds per foot is 1152 foot-pounds.
