Understanding Pump Work Calculation

This problem involves calculating the work done by a pump in lifting a certain volume of water to a specific height over a given time period. We need to determine the total work done over a longer duration (one hour) based on the work done in a shorter duration (one minute).

Key Concepts for Pump Work

• Work Done: In physics, work is done when a force causes a displacement. The standard formula for work is Work = Force × Distance.
• Force: In this case, the force exerted by the pump is against the weight of the water being lifted. Weight is calculated as Weight = Mass × Acceleration due to gravity (g).
• Mass: The mass of water can be determined from its volume and density. The density of water is approximately $1 \text{ kg/liter}$.
• Units: The question uses "kg metres" as the unit for work. This unit typically arises from multiplying mass (kg) by distance (m). While standard work units are Joules (kg⋅m²/s²), the options suggest a simplified calculation where Work = Mass × Height is used, possibly omitting the gravitational constant '$g$' for the purpose of this specific problem or considering 'kg metres' as a unit of potential energy relative to a reference point, scaled by mass. We will proceed using this interpretation based on the provided options.

Given Information

• Volume of water lifted per minute: $200 \text{ liters}$
• Height through which water is lifted: $300 \text{ meters}$
• Time duration for the given lift: $1 \text{ minute}$

Step-by-Step Calculation

Step 1: Determine the Mass of Water Lifted Per Minute

Assuming the density of water is $1 \text{ kg/liter}$, the mass of 200 liters of water is:

$$ \text{Mass} = \text{Volume} \times \text{Density} $$

$$ \text{Mass} = 200 \text{ liters} \times 1 \text{ kg/liter} = 200 \text{ kg} $$

Step 2: Calculate the Work Done Per Minute

Using the interpretation that Work = Mass × Height based on the units in the options:

$$ \text{Work done per minute} = \text{Mass} \times \text{Height} $$

$$ \text{Work done per minute} = 200 \text{ kg} \times 300 \text{ m} $$

$$ \text{Work done per minute} = 60000 \text{ kg m} $$

So, the pump does 60,000 kg metres of work every minute.

Step 3: Calculate the Total Work Done in One Hour

We need to find the work done in one hour. Since there are 60 minutes in an hour, we multiply the work done per minute by 60.

$$ \text{Work done per hour} = (\text{Work done per minute}) \times (\text{Number of minutes in an hour}) $$

$$ \text{Work done per hour} = 60000 \text{ kg m/min} \times 60 \text{ min} $$

$$ \text{Work done per hour} = 3600000 \text{ kg m} $$

Conclusion

The pump can do 3,600,000 kg metres of work in one hour.