A chain 64 meters long whose mass is 20 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 3 meters of the chain to the top of the building?

To determine the amount of work required to lift the top 3 meters of the chain to the top of the building, we can use the concept of gravitational potential energy.

The potential energy (PE) of an object at a height h above the ground can be given by the equation:

PE = mgh

Where:
m is the mass of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height of the object above the ground

In this case, we need to calculate the increase in potential energy by lifting the top 3 meters of the chain. Since the chain is already hanging over the edge of the building, its initial height is 64 meters, and we want to raise it by an additional 3 meters. Therefore, the new height is 64 + 3 = 67 meters.

First, we need to determine the mass of the portion of the chain being lifted. We can use the given mass of the entire chain (20 kilograms) to calculate the mass per unit length of the chain.

Mass per unit length = total mass / total length
Mass per unit length = 20 kg / 64 m

Next, we can use the mass per unit length to calculate the mass of the portion being lifted.

Mass of lifted portion = mass per unit length x lifted height
Mass of lifted portion = (20 kg / 64 m) x 3 m

Once we have the mass of the lifted portion, we can substitute it into the potential energy equation to calculate the required work.

Work = PE = mgh
Work = (mass of lifted portion) x g x (lifted height)
Work = [(20 kg / 64 m) x 3 m] x 9.8 m/s^2

Now we can simplify and calculate the work required:

Work = [(20 kg / 64 m) x 3 m] x 9.8 m/s^2

lol k.