Calculating Work in Lifting a Chain and Concrete
How much work does it take to wind up the chain and concrete to the top of the building?
At the bottom of the chain is a 120 kg bag of concrete and the chain has a density of 3 kg/m. The chain is hanging from a tall building with a length of 25 meters.
Answer:
The work required to wind up the chain and concrete to the top of the building is approximately 31,470 Joules.
Calculating the work required to lift the chain and concrete involves considering their gravitational potential energy. The work done is equal to the change in potential energy, which can be calculated using the formula:
Work = Change in potential energy = mgh
Where:
- m is the total mass of the chain and the concrete
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height the chain is lifted (25 meters in this case)
Given the chain density of 3 kg/m and the concrete mass of 120 kg, the total mass is 3 kg/m x 25 m + 120 kg = 195 kg.
Plugging in the values to the formula:
Work = 195 kg * 9.8 m/s^2 * 25 m
Calculating the above equation gives us the work required as approximately 31,470 Joules.