Video Transcript
An empty water tank has a rectangular base with side lengths of 1.2 metres and 2.3 metres. The weight of the tank applies a pressure of 350 pascals to the surface it is resting on. What is the weight of the tank?
Okay, so in this question, we’ve been told that we’ve got an empty water tank. And the tank has a rectangular base. So, that’s this face over here, which has side lengths of 2.3 metres and 1.2 metres. As well as this, we’ve been told that the tank is resting on a surface. So, lets draw the surface in here because we’ve been told that the weight of the tank applies a pressure of 350 pascals to the surface it’s resting on.
Now, the weight of the tank is acting in a downward direction, and we’ll call it 𝑊. And this weight of the tank is exactly the force that the tank itself exerts on the surface that it’s resting on. As well as this, the area over which that weight is distributed is simply the area of the base of the tank. This is because all of the tank’s weight, the weight 𝑊, is the force applied to the surface that the tank is resting on. And that force is distributed over the entire base.
Now at this point, we can recall that the pressure exerted on a surface, which we’ll call 𝑃, is given by the force exerted on that surface divided by the area of that surface. So, in our situation where we’ve got the tank exerting a force, that’s the weight of the tank, onto the surface that it’s resting on. We know that the pressure exerted by the weight of the tank is equal to the weight of the tank divided by the area of the base of the tank. Because, once again, that area is the area over which the force is distributed.
Now, in the question, we’ve actually already been told the pressure exerted by the weight of the tank. And as well as this, we have enough information to work out the area of the base of the tank. Because we know the side lengths of the base of the tank. So, based on all of this, we can work out the force exerted or, in other words, the weight of the tank. Which is exactly what we need to do in this question.
So, first of all, let’s start by finding the area of the base of the tank. Now we’ve been told that the tank has a rectangular base. Therefore, if we look at the tank from above, what we’ll see is a rectangular base which is 2.3 metres by 1.2 metres. And so, we can recall that the area of a rectangle is found by multiplying the length by the width. So, in this situation, it’s 1.2 metres multiplied by 2.3 metres. Now this ends up being 2.76 metres squared. Which means, at this point, we know the pressure, which is 350 pascals, and the area, which is 2.76 metres squared.
So, we can rearrange the equation to find the force exerted, which is equal to the weight of the tank. And we can do this by multiplying both sides of the equation by 𝐴, the area. This way, 𝐴 cancels on the right-hand side. And what we’re left with is that the area multiplied by the pressure is equal to the force. Then all we need to do is to sub in the values.
We can say that the force exerted, which is equal to the weight of the tank, is equal to the area, 2.67 metres squared, multiplied by the pressure, 350 pascals. Then we can notice that we’re working in base units. Metre squared is the base unit of area. And pascal is the base unit of pressure. Which means that the force that we find on the left-hand side, or in other words the weight, is going to be in its own base unit, which is the newton. Therefore, evaluating the right-hand side of the equation, we find that the weight of the block is 966 newtons. And this is the final answer to our question.
