Video: Force and Pressure

A pressure of 20 Pa is applied by an 8000 N force to a square area. What is the length of a side of the square?

02:04

Video Transcript

A pressure of 20 pascals is applied by an 8000-newton force to a square area. What is the length of a side of the square?

Okay, so in this question, we’ve got a square area, which we can draw something like this if we’re looking at it slightly side-on. And we’ve been told that a force of 8000 newtons is applied to this area. This results in a pressure of 20 pascals. Now at this point, we can recall the relationship between pressure, force, and area.

Pressure is defined as the force per unit area or in other words the force exerted on an area divided by that area. So using this equation, because we know that the pressure exerted on this blue area is 20 pascals and the force exerted is 8000 newtons, we can calculate the area. We can do this by rearranging the equation for which we have to multiply both sides by 𝐴 divided by 𝑃. In this case, the 𝑃s on the left-hand side cancel and the 𝐴s on the right-hand side cancel. What this leaves us with is that area 𝐴 is equal to the force 𝐹 divided by the pressure 𝑃.

Therefore, we can plug in the values for the force which is 8000 newtons and the pressure which is 20 pascals. And since we’re working in base units for both the pressure and the force, our answer ends up being 400 meters squared, where meter squared is the base unit of area. So at this point, we’ve worked out that the total blue area is 400 meters squared.

However, what we’ve been asked to do is to find the length of one of the sides. Luckily though, we’ve been told that this area is actually a square. And hence, we know that the lengths of all of the sides are equal. So we can say that 𝑥 is the length of one of the sides and therefore it’s also the length of all of the sides. Then, we can work out that the area of a square is found by multiplying its length by its width, which because it’s a square, it’s 𝑥 in both cases. Therefore, we can say that the area is equal to the length squared.

And hence, if we want to find the length of one of the sites which is 𝑥, we need to rearrange this equation by taking the square root of both sides. This way, the square root on the right-hand side cancels with the squared. And what we’re left with is that the square root of the area of the square is equal to the length of one of its sides. But then, we’ve just calculated the area to be 400 meters squared. Therefore, the length of one of the sides of the square is the square root of 400 meters squared. And this ends up being 20 meters, which also happens to be the final answer to our question.

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