A pump lifts water from a lake to a large tank 20 m above the lake. How much work against gravi

step 1 Hello. So in this problem, we have a water pump that is pumping water out of this lake here so t

A pump lifts water from a lake to a large tank 20 m above...

A pump lifts water from a lake to a large tank $20 \mathrm{~m}$ above the lake. How much work against gravity does the pump do as it transfers $5.0 \mathrm{~m}^{3}$ of water to the tank? One cubic meter of water has a mass of $1000 \mathrm{~kg}$.

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. When an object is lifted to a higher elevation, its gravitational potential energy increases by an amount equal to the product of its mass, the acceleration due to gravity, and the height it is raised. This concept is central to calculating the work done against gravity when an object is elevated.

Work Against Gravity

Work is defined as the product of a force and the distance over which it is applied. In the context of lifting objects, the work done against gravity is essentially the increase in gravitational potential energy. For any mass being raised a certain height, the work required is determined by multiplying the mass, the gravitational acceleration, and the height.

Density and Mass-Volume Relationship

Density is a property that relates the mass of a substance to its volume. In many practical situations, quantities like volume are given, and the corresponding mass must be determined using the substance's density. This conversion is crucial in physics problems where the mass is needed to calculate forces or energy changes, such as when computing the work done in lifting a given volume against gravity.

Acceleration Due to Gravity

The acceleration due to gravity is a constant that represents the rate at which objects accelerate toward the Earth. It is typically approximated as 9.8 m/s² in calculations involving gravitational force or potential energy. This constant is a key factor in determining the force of gravity acting on any mass, thereby affecting the work required to change the vertical position of that mass.

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