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I have recently been studying pressure and the basic pressure formula:

$\ P= F\ /A$

and I was wondering why it does not include direction of the force in the formula and I played around with it for a bit and I got the formula:

$\ P= F\sin( \theta)\ /A$

(not including calculus or varying pressure or area for now). Is this formula correct?

And if so how could I change it to account for a change in area or force?

For example here 30 degrees is theta and the hypotenuse is 10N

enter image description here

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  • $\begingroup$ I think pressure is equal to perpendicular component of the force divided by the area. $\endgroup$
    – user240696
    Commented Feb 8, 2020 at 10:35
  • $\begingroup$ yes sin(theta) would give you the perpendicular value of the force if you take the value of the force as the hypotenuse. $\endgroup$
    – Manav
    Commented Feb 8, 2020 at 10:43
  • $\begingroup$ Please specify with which (vertical or horizontal) the force makes an angle of $\theta$ in your question. $\endgroup$
    – user240696
    Commented Feb 8, 2020 at 10:44
  • $\begingroup$ I edited the question to include an example $\endgroup$
    – Manav
    Commented Feb 8, 2020 at 10:57
  • $\begingroup$ Yes your equation is correct. $\endgroup$
    – user240696
    Commented Feb 8, 2020 at 10:58

1 Answer 1

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From the wikipedia page: Pressure is the amount of force applied at right angles to the surface of an object per unit area.

So your formula including sin(θ) is correct.

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  • $\begingroup$ What about this And if so how could I change it to account for a change in area or force? ? $\endgroup$
    – user240696
    Commented Feb 8, 2020 at 11:27
  • $\begingroup$ Pressure is an instantaneous magnitude, i.e. if the force or the area change, the pressure at each instant is the value of F/A at that precise instant. If these are functions of time, then P(t) = F(t)/A(t). $\endgroup$
    – Leo
    Commented Feb 8, 2020 at 11:30
  • $\begingroup$ Well that's really what I wrote in my comment but OP didn't reply therefore I deleted it and asked him this $\endgroup$
    – user240696
    Commented Feb 8, 2020 at 11:32
  • $\begingroup$ Sorry I had logged off my computer by that time and i didn't see your comment. $\endgroup$
    – Manav
    Commented Feb 9, 2020 at 11:23

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