Question

An aquarium 4 m long, 2 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the facts that the density of water is 1000 kg/m3 and g≈9.8 m/sec∧2.)

Answer 1

The work needed to pump half the water out of an aquarium with given dimensions, using the provided water density and approximation for gravity, would be 39,200 Joules.

Step-by-step explanation:

To find the work needed to pump half of the water out of the aquarium, we first need to determine how much water is in the aquarium, and then how much work is required to remove half of it.

The volume of the aquarium is 4m * 2m * 1m = 8 cubic meters (m^3). So, the mass of the water (given that the density of water is 1000 kg/m^3) is 8m^3 * 1000 kg/m^3 = 8000 kg. As we only need to remove half of the water, the relevant mass is 4000 kg.

The work done on an object is equal to the force applied to it times the distance over which that force is applied. In this case, work is done by lifting the water against gravity. Thus, the work can be calculated using the formula work = mgh, where m is the mass of the object (4000 kg), g is acceleration due to gravity (9.8 m/sec^2), and h is the height to which the object is lifted (1m in this case).

Therefore the work done to pump out half the water from the aquarium is 4000 kg * 9.8 m/sec^2 * 1 m = 39200 Joules.

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