Video: Force and Pressure

Which of the following formulas correctly shows the relationship between an applied force, the pressure that the force produces, and the area on which the force acts? [A] 𝑝 = 𝐴/𝐹 [B] 𝑝 = 𝐹/𝐴² [C] 𝑝 = 1/(𝐹𝐴) [D] 𝑝 = 𝐹𝐴 [E] 𝑝 = 𝐹/𝐴

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Video Transcript

Which of the following formulas correctly shows the relationship between an applied force, the pressure that the force produces, and the area on which the force acts?

Okay, so let’s first imagine that we’ve got this surface which has an area, which we’ll call 𝐴. And on this surface with area 𝐴, we exert a force, which we will call 𝐹. Now, in a situation like this, the pressure exerted by this force on this area is defined as the force exerted per unit area. Or in other words, the pressure exerted is equal to the force exerted on the area divided by the area itself. This is because the equation then gives us the amount of force exerted for every single unit of area that we have.

In other words, if a force 𝐹 is exerted over the total area 𝐴 and is distributed over the entire area, then that’s equivalent to, let’s say, this being a unit of area and having a smaller force exerted on that area. And that same smaller force is exerted on every single unit of area, which is equivalent to this large force 𝐹 being exerted on the whole area 𝐴. So this equation gives us the definition of pressure. And out of all the options A to E, we can say that it matches with option E.

Therefore, our final answer is that the pressure produced by the force is equal to that force divided by the area over which that force is distributed.

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