A construction worker has to pump water from reservoir A to reservoir B over a hill using an electric water pump, as illustrated in the diagram below - NSC Technical Sciences - Question 4 - 2024 - Paper 1

The force applied on the water can be calculated using the formula: $F_{pump} = F_g$ Since the water is moving at constant velocity, the force exerted by the pump equals the weight of the water. Therefore: $F_{pump} = 8330 ext{ N upwards}$

To find the velocity of the water, we can use the power formula relating power ($P$), force ($F$), and velocity ($v$): $P = F imes v$ Rearranging gives: $v = \frac{P}{F}$ Substituting the values: $v = \frac{7200}{8330} \approx 0.865 ext{ m/s upwards}$

The principle of conservation of mechanical energy states that the total mechanical energy in an isolated system remains constant. This means that the sum of potential energy and kinetic energy in a closed system will not change over time if only conservative forces are acting.

The work done by the gravitational force ($W_g$) can be calculated using: $W_g = F_g imes h imes ext{cos}( heta)$ Where:

• $F_g = 8330 ext{ N}$
• $h = 6 ext{ m}$
• $heta = 0$ degrees (as the motion is vertical). Hence: $W_g = 8330 imes 6 imes ext{cos}(0) = 49980 ext{ J}$

The work done by the gravitational force is the energy transferred when lifting the water against gravity. In our calculation, we considered the force due to gravity acting downwards and the displacement upwards. By using the formula for work: $W = F imes d imes ext{cos}( heta)$ Where $d$ is the height moved, we see that the gravitational force plays a critical role in determining the energy needed to lift the 850 kg of water to the specified height.

The gravitational potential energy ($E_p$) can be calculated using: $E_p = mgh$ Where:

• $m = 274 ext{ kg}$
• $g = 9.8 ext{ m/s}^2$
• $h = 12.58 ext{ m}$ Thus:

The mechanical energy at the 6 m point can be calculated in a similar way: $E_{m} = E_{p} + E_{k}$ Where $E_{p}$ is the potential energy at this height and $E_{k}$ is the kinetic energy. Since the water is moving, we also need to account for its kinetic energy using: $E_k = \frac{1}{2} mv^2$ Calculating the kinetic energy at the 6 m height with $v$ being the velocity previously calculated, we can substitute these values into the overall mechanical energy formula.