1. An electric pump, used to obtain water from 20 metres below the ground, is marked 5000W.

a) If the pump operates as rated, how much energy is used to pump water every second?
b) Describe the energy conversions that take place when the pump is used.
c) What is the maximum mass of water that can be brought to the surface every second, and then discharged at 10 metres per second.

a) To calculate the energy used by the pump every second, we need to convert the power rating from watts to joules per second (or watts to kilojoules per second).

1 watt (W) = 1 joule per second (J/s)

Therefore, the energy used to pump water every second can be calculated as:

Energy = Power × Time
Energy = 5000 W × 1 s
Energy = 5000 J/s

b) The energy conversions that take place when the pump is used involve the conversion of electrical energy to mechanical energy and ultimately to potential energy:

1. The electrical energy is converted to mechanical energy by the electric pump. This is achieved by converting the electrical input into the necessary rotational motion of the pump's impeller.
2. The mechanical energy is then converted to potential energy as the pump lifts the water from 20 meters below the ground to the surface.
3. The potential energy of the water can later be converted to other forms of energy when it is used or discharged.

c) To calculate the maximum mass of water that can be brought to the surface every second, we need to consider the work done by lifting the water against gravity.

The work done (W) is given by the formula:

Work = Force × Distance

In this case, the distance is 20 meters and the force required is equal to the weight of the water being lifted. The weight can be calculated using the formula:

Weight = Mass × Gravity

Assuming that the gravitational acceleration is approximately 9.8 m/s², we can calculate the maximum mass of water that can be brought to the surface every second:

Work = Force × Distance
Force = Weight = Mass × Gravity
Work = Mass × Gravity × Distance
Work = Mass × 9.8 m/s² × 20 m

The work done by the pump is equal to the energy used by the pump, which we calculated earlier as 5000 J/s. Equating these two values, we can solve for the maximum mass:

5000 J/s = Mass × 9.8 m/s² × 20 m

Simplifying the equation:

Mass = (5000 J/s) / (9.8 m/s² × 20 m)
Mass = 25.51 kg/s

Therefore, the maximum mass of water that can be brought to the surface every second is approximately 25.51 kilograms, assuming all the energy is used solely for lifting the water.

a) To find the energy used by the pump every second, we need to calculate the power consumption. Power is given by the equation:

Power = Energy / Time

The pump is marked 5000W, which means it consumes 5000 Joules of energy every second. Therefore, the energy used to pump water every second is 5000 Joules.

b) When the electric pump is used, there are various energy conversions taking place. The electrical energy from the power source is converted into mechanical energy, which drives the pump's mechanism. The mechanical energy is then used to lift water from 20 meters below the ground to the surface. So, the energy conversions involve electrical energy being converted to mechanical energy and then into potential energy of the water.

c) To calculate the maximum mass of water that can be brought to the surface every second, we need to consider the power and velocity of the water. The power used by the pump is 5000 Watts, and we assume all the power is used to lift the water vertically. From the equation:

Power = Force * Velocity

We can rearrange the equation to:

Force = Power / Velocity

Given that the velocity at which the water is discharged is 10 meters per second, we substitute the values:

Force = 5000 / 10 = 500 Newtons

Since force is equal to mass multiplied by acceleration, and the acceleration due to gravity is approximately 9.8 m/s², we can rearrange the equation:

Mass = Force / Acceleration

Substituting the values:

Mass = 500 / 9.8 = 51.02 kg

Therefore, the maximum mass of water that can be brought to the surface every second and discharged at 10 meters per second is approximately 51.02 kg.