Question

The pressure P exerted by a force varies inversely as the area A on which the force is applied. If 16 N/ft2 of pressure is exerted by a force on an area of 3 ft2 , what is the pressure exerted by the same force on an area of 6 ft2?

A) 8 N/ft2
B) 16 N/ft2
C) 4 N/ft2
D) 32 N/ft2

Answer 1

The first piece of information tells you that
16 = C / 3
Solve for C
C=16×3=48
Now find P if A = 6. and C=48
P = C/6
P = 48/6
P = 8 N/ft2

Answer 2

A) 8 N/ft2

Explanation:

Pressure is the normal force per unit area, that is, it is equivalent to the force acting on the surface unit, and is given by:

`P=(F)/(A)`

Where:

`P=Pressure\\F=Normal\hspace{3}force\\A=Area\hspace{3} where \hspace{3}force\hspace{3} is \hspace{3}applied.`

In the first case:

`P=16N/ft^2\\A=3ft^2`

Using the previous equation and solving for
`F` :

`F=P*A=16*3=48N`

Now, for the second case, since the force is the same applied in the first case, then:

`P=(F)/(A) =(48)/(6) =8N/ft^2`

Therefore the answer is:

A) 8 N/ft2