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