A pressure of 400 pascals is applied to an area of 2.5 meters squared. What force applies this pressure?
Okay, so in this question, we’re told that we have a pressure with a value of 400 pascals. We’ll label this pressure as 𝑃 so that we have 𝑃 is equal to 400 pascals. We’re also told that this pressure is applied over an area of 2.5 meters squared. Let’s label this area as 𝐴 so that we have 𝐴 is equal to 2.5 meters squared. We’re asked to work out what force applies this pressure.
So, we know that we have some surface with an area of 𝐴 equals 2.5 meters squared. We also know that we have some force that we’ll label as 𝐹, which acts all over this area, and that this force results in a pressure of 𝑃 equals 400 pascals. We can recall that pressure is defined as force per unit area. Mathematically, we can write this as pressure, 𝑃, is equal to 𝐹, so that’s the force, divided by 𝐴, the area of the surface over which the force acts.
In our case, we know the value of 𝑃 and we know the value of 𝐴. We’re trying to find the value of the force 𝐹. This means that we need to take this equation and rearrange it to make 𝐹 the subject. To do this, we’ll multiply both sides of the equation by 𝐴. Then, on the right-hand side, the 𝐴 in the numerator cancels with the 𝐴 in the denominator. And we’re left with an equation that says 𝐴 multiplied by 𝑃 is equal to 𝐹, which we can also write as 𝐹 is equal to 𝐴 multiplied by 𝑃.
Now, we just need to substitute in our values for the pressure 𝑃 and the area 𝐴 into the right-hand side of this equation. Substituting in that 𝐴 is equal to 2.5 meters squared and 𝑃 is equal to 400 pascals, we get that the force 𝐹 is equal to 2.5 meters squared multiplied by 400 pascals.
At this point, we can notice that both the area and the pressure are expressed in their SI base units. So, for area, that’s units of meter squared and for pressure, that’s pascals. Since both of the terms on the right-hand side of our equation for the force are in their SI base units, then the force is also going to be in its own SI base unit. The SI base unit for force is the newton. So, we’re going to get a value for our force 𝐹 in units of newtons. And when we do the multiplication, we find that 2.5 multiplied by 400 gives us a value of 1000.
And so, our final answer to the question is that the force has a value of 1000 newtons.