If a person lifts a 21.9 kg bucket very slowly from a well and does 8.3 kJ of work on the bucket, how deep is the well?
To determine the depth of the well, we can use the concept of work-energy principle. According to this principle, the work done on an object is equal to the change in its potential energy.
In this case, the person does work on the bucket by lifting it. The work done, W, is given as 8.3 kJ (kilojoules).
The potential energy of an object near the surface of the Earth is given by the formula:
Potential energy = mass × acceleration due to gravity × height
Here, the mass of the bucket is given as 21.9 kg, and the acceleration due to gravity on Earth is approximately 9.8 m/s^2.
So, we can rearrange the formula to solve for height:
Height = Potential energy / (mass × acceleration due to gravity)
First, we need to convert the given work done from kilojoules to joules:
8.3 kJ = 8.3 × 1000 J = 8300 J
Next, we can substitute the values into the formula to calculate the height:
Height = 8300 J / (21.9 kg × 9.8 m/s^2)
Now, we can perform the calculation:
Height = 378.10 m
Therefore, the depth of the well is approximately 378.10 meters.