Calculate the work done in kilojoules to lift 50 cubic meters of water to a height of six meters, given that the density of water is 1,000 kilograms per meter cubed. Take 𝑔 equal to 9.8 meters per second squared.
We begin by recalling that work done can be calculated by multiplying force by distance. The direction of both the force and distance matters such that the work can be negative, positive, or zero. The standard units of force and distance are newtons and meters, respectively. This means that work is measured in newton meters, and these are more commonly referred to as joules.
Let’s begin by sketching the scenario in this question. A crate of water is being lifted to a height of six meters. We are told that the volume of water is 50 cubic meters. And we are also told that the density of water is 1,000 kilograms per cubic meter. We recall that the mass of an object is equal to its density multiplied by its volume. We can therefore calculate the mass of the water by multiplying 1,000 by 50. This is equal to 50,000 kilograms.
The downward force of the water is equal to the weight 𝑊. We know that the weight of an object is equal to its mass multiplied by gravity. This means that the weight 𝑊 is equal to 50,000 multiplied by 9.8. This is equal to 490,000 newtons. In order to lift the water, we will need an equal force 𝐹 acting in the opposite direction. If we consider vertically upwards to be the positive direction, the work done is therefore equal to 490,000 multiplied by six. The force in this direction is 490,000, and the water is being lifted six meters in this direction. This is equal to 2,940,000. And as already mentioned, this is the work done in joules. As we are asked to give our answer in kilojoules, we need to divide 2,940,000 by 1,000.
The work done to lift 50 cubic meters of water to a height of six meters is 2,940 kilojoules.