If a woman lifts a 16.2 kg bucket from a well and does 6.33 kJ of work, how deep is the well? Assume that the speed of the bucket remains constant as it is lifted.

To find the depth of the well, we can use the concept of work and energy. The work done by the woman in lifting the bucket is equal to the change in potential energy of the bucket as it moves from the bottom of the well to the surface.

The work done can be calculated using the formula:

Work = Force × Distance

In this case, the force is equal to the weight of the bucket, and the distance is the depth of the well. The weight of an object is equal to its mass multiplied by the acceleration due to gravity.

Weight = Mass × Gravity

Using this information, we can set up the equation:

Work = Weight × Distance

6.33 kJ = (16.2 kg × 9.8 m/s^2) × Distance

Simplifying the equation:

6.33 kJ = 158.76 kg⋅m^2/s^2 × Distance

Converting kilojoules to joules:

6.33 kJ = 6330 J

Now we can solve for Distance:

Distance = (6330 J) / (158.76 kg⋅m^2/s^2)

Distance = 39.872 meters

Therefore, the depth of the well is approximately 39.872 meters.