A pump is needed to lift 75 0 L of water per minute a distance of 25.0 m . What power (in kW )

step 1 In this problem we are given it volume of water is equal to 750 liters is 1 liter is equal to 1

A pump is needed to lift 75 0 L of water per minute a...

A pump is needed to lift $75 \overline{0} \mathrm{~L}$ of water per minute a distance of $25.0 \mathrm{~m} .$ What power (in $\mathrm{kW}$ ) must the pump be able to deliver? (1 $\mathrm{L}$ of water has a mass of $1 \mathrm{~kg}$.)

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Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When an object with mass m is elevated by a height h, the work done (or energy required) is given by the product m × g × h, where g is the acceleration due to gravity. This principle is central to calculating the energy necessary to lift any mass against gravity.

Power

Power is the rate at which energy is transferred or converted, defined as the amount of work done per unit time. In problems involving lifting objects against gravity, once the total energy required (from gravitational potential energy) is computed, it is divided by the time interval to determine the power output needed. It is typically expressed in watts (joules per second) or kilowatts.

Unit Conversion

Unit conversion is critical in physics to ensure consistency in calculations. For example, converting volume to mass (using density, such as 1 liter of water equaling 1 kilogram), and converting time units (from minutes to seconds) are essential steps to align all quantities into compatible SI units.

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