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