'Melvin lifts a 28.9 kg bucket from a well and does 3.41 kJ of work. how deep is te well'

work done = mgh

3410 = 28.9 *10*h

h = 3410/(289)

h = 11.79m

To calculate the depth of the well, we need to use the work-energy principle. The work done on an object is equal to its change in potential energy. In this case, the work done by Melvin when lifting the bucket is equal to the change in potential energy of the bucket at a certain height.

The formula for calculating work done is:

Work = Force × Distance × cos(θ),

where the force is the weight of the bucket (mass × acceleration due to gravity), the distance is the depth of the well, and θ is the angle between the applied force and the displacement (which is generally 0° when lifting straight up).

Given that Melvin lifts a 28.9 kg bucket and does 3.41 kJ of work, we can convert the work into Joules:

3.41 kJ = 3.41 × 10^3 J.

We know that the weight of the bucket (force) is given by the formula:

Weight = mass × acceleration due to gravity.

Assuming the acceleration due to gravity is 9.8 m/s², we can calculate the weight:

Weight = 28.9 kg × 9.8 m/s².

Now, we can substitute these values into the equation: Work = Force × Distance × cos(0°).

3.41 × 10^3 J = (28.9 kg × 9.8 m/s²) × Distance × cos(0°).

Simplifying the equation:

3.41 × 10^3 J = 282.82 kg·m/s² × Distance × 1.

Rearranging the equation to solve for Distance:

Distance = (3.41 × 10^3 J) / (282.82 kg·m/s²).

Calculating the distance:

Distance = 12.04 meters.

Therefore, the depth of the well is approximately 12.04 meters.