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A pressure of 75 pascals is applied by a 3000-newton force.
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What area is the force applied to?
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Okay, so in this question, we can first imagine that we’ve got some surface with an area which we’ll call 𝐴.
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And then, we can imagine that a 3000-newton force is applied to this area.
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Let’s call that force 𝐹.
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And we can say that the force is equal to 3000 newtons.
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Now, we’ve been told that as a result of this force of 3000 newtons applied over the area 𝐴, the pressure that results is 75 pascals.
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And based on that information, we need to find the value of 𝐴.
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So to do this, we can recall that pressure is defined as the force applied per unit area.
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Or in other words, pressure is equal to force divided by area because the idea here is that a certain force is applied over a certain area and that force gets distributed over the entire area.
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So using this equation, we can rearrange to find the area of the surface.
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And to do this, we multiply both sides of the equation by 𝐴 divided by 𝑃.
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This way, 𝑃s on the left-hand side cancel and 𝐴s on the right-hand side cancel.
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And what we’re left with is that the surface area is equal to the force exerted divided by the pressure.
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Then, we can substitute our values for the force, 3000 newtons, and the pressure, 75 pascals.
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And at this point, we can notice that we’re working in base units, in newtons for force and pascals for pressure.
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Well, in that case, the answer to our left-hand side of the equation — that’s the area — is going to be in its own base unit, which is meter squared.
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Therefore, evaluating the fraction on the right-hand side, we find that the area 𝐴 is equal to 40 meters squared.
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And that is the final answer to our question.