Explanation:
The pressure of an object is calculated as follows: [tex]P = \frac{F}{A}[/tex]
The area of test tube stopper is A= π[tex]r^{2}[/tex]
Since radius is half the diameter we have the following:
R = [tex]\frac{1.20 cm}{2}[/tex] = 0.60 cm
Thus the area of the test tube becomes:
A = π [tex]( 0.60 Cm)^{2}[/tex]
= π [tex](0.006 m) ^{2}[/tex]
= 1.14 * [tex]10^{-4} m^{2}[/tex]
Now the force from the outside of the tube.
[tex]F_{out} = P_{out} A[/tex]
= [tex]( 1.013 * 10^{5} Pa ) ( 1.14 * 10^{-4} m^{2} )[/tex]
= 11.55N
The net upward force on the stopper is equal to the difference of force exerted by pressure from inside of the tube and that from the outside.
[tex]F_{Net} = F_{In} - F_{Out}[/tex]
[tex]F_{In} = F_{Net} + F_{Out}[/tex]
[tex]F_{In} = 11.5N + 11.55N[/tex]
= 23.1 N
