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

Respuesta :

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:

A) 8 N/ft2

Step-by-step 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:

[tex]P=\frac{F}{A}[/tex]

Where:

[tex]P=Pressure\\F=Normal\hspace{3}force\\A=Area\hspace{3} where \hspace{3}force\hspace{3} is \hspace{3}applied.[/tex]

In the first case:

[tex]P=16N/ft^2\\A=3ft^2[/tex]

Using the previous equation and solving for [tex]F[/tex] :

[tex]F=P*A=16*3=48N[/tex]

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

[tex]P=\frac{F}{A} =\frac{48}{6} =8N/ft^2[/tex]

Therefore the answer is:

A) 8 N/ft2