Which of the following is the correct unit for pressure? 1) newton, 2) newton meter, 3) newtons per meter, 4) joule, 5) pascal.
Okay, so in this question, we’re trying to find the correct unit for pressure. So let’s go through them one by one and discuss what each of these units are for.
Let’s start with number one — the newton. Well, the newton is a unit of force, not pressure. So number one is not the answer that we’re looking for. Let’s look at number two then — newton meter. Well, we’ve already said that newton is a unit of force from number one. And we can recall that meter is a unit of distance.
Now, the newton meter can be a unit for a couple of different kinds of quantities. Depending on the context of the situation that quantities could either be, the work done on an object when we apply a force 𝐹 to the object and it moves a distance 𝑑, in which case, the work done 𝑊 is defined as the force applied multiplied by the distance moved. And this work done will have units of newtons multiplied by meters because force has unit of newtons and distance has unit of meters.
So newton meters could be a unit of work done or if we had a situation, where we had something that could rotate, let’s say a plank and we applied to force 𝐹 at distance 𝑑 away from the point at which this plank would rotate, then we would be applying a torque to this plank. And this torque would be 𝑇, the torque, is equal to the force multiplied by the perpendicular distance 𝑑 between the point at which the force is applied, which is here, and the point at which the plank rotates, which is here.
And once again, torque has a unit of newtons multiplied by meters. So as we said earlier, depending on the context, newton meters could be a unit of either torque or work done. However, neither torque nor work down is the same as pressure. So number two is not the answer we’re looking for either.
Number three then, newtons per meter. Now, one example of a quantity which has the unit newtons per meter is the spring constant of a string because remember the force applied to a spring which we’ll call 𝐹 is equal to the spring constant of the spring 𝑘 multiplied by the extension of the spring. So let’s say the natural length of the spring is this distance here.
Well, then, the force applied is equal to the spring constant multiplied by the extension of the spring which is 𝑥 — in other words, how much longer the spring is relative to its natural length. So if we rearrange the equation by dividing both sides by 𝑥, then the 𝑥s cancel on the right-hand side. And we’re left with the force divided by the extension is equal to the spring constant.
So what are the units of spring constant? Well, we’ve said earlier that force has a unit of newtons and extension will have a unit of meters. So we’ve got newtons per meter. However, this also is not the same thing as a pressure. So number three is not our answer either.
Moving swiftly onto number four then, we’ve got the joule. Now, the joule is a unit of energy, not pressure. So as swiftly as we moved onto number four, we can move away from it. What this means is that number five must be the right answer. And in fact, it is. The correct unit of pressure is the pascal.
Now just as a quick aside, remember that pressure which we’ll call 𝑃 is defined as the force per unit area. And the unit of pressure which we’ll say is one pascal is simply defined as one newton which is the force divided by one meter squared which is an area. And this is a useful fact to remember.
Anyway, the final answer to our question is that the pascal is the correct unit for pressure.