how would the pressure (exerted by a force on an area) change if the area is doubled keeping the trust constant?
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Pressure is defined as the force acting per unit area of a surface. It is always perpendicular to the surface.
Hence, P = F/A
Here, P is the pressure exerted per unit area of a surface of total area A due to a force F.
Let P be the initial pressure on area A due to constant force F
P = F/A
Let P' be the pressure when the area of contact is doubled
P' = F/2A
Now, dividing these two equations
P/P' = (F/A)/(F/2A)
A bit of mathematics, and
P = 2P'
Or
P' = P/2
So, the pressure per unit area gets halved.
Hence, P = F/A
Here, P is the pressure exerted per unit area of a surface of total area A due to a force F.
Let P be the initial pressure on area A due to constant force F
P = F/A
Let P' be the pressure when the area of contact is doubled
P' = F/2A
Now, dividing these two equations
P/P' = (F/A)/(F/2A)
A bit of mathematics, and
P = 2P'
Or
P' = P/2
So, the pressure per unit area gets halved.
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