A chain 27 feet long whose weight is 74 pounds is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the entire chain to the top of the building?
To find out how much work is required to lift the entire chain to the top of the building, we need to take into consideration the weight of the chain and the distance it needs to be lifted.
The work done to lift an object is given by the formula:
Work = Force × Distance
In this case, the force we need to lift is the weight of the chain, which is 74 pounds. The distance it needs to be lifted is the height of the building, which is not given in the question.
To find the height of the building, we can use the Pythagorean theorem, considering the chain as the hypotenuse of a right triangle.
Let's assume the chain hangs in a straight line from the edge of the building to the ground. We can form a right triangle where one side is the length of the chain, 27 feet, and the other side represents the height of the building.
Using the Pythagorean theorem:
height² = hypotenuse² - base²
height² = 27² - 0²
height² = 729
height = √729
height = 27 feet
Therefore, the height of the building is 27 feet.
Now we can calculate the work required to lift the entire chain to the top of the building:
Work = Force × Distance
Work = 74 pounds × 27 feet
Work = 1,998 pounds × feet
Therefore, the work required to lift the entire chain to the top of the building is 1998 pound-feet.