We would consider the hydraulic lift where the pressure is the same on the
master ad slave cylinder but force changes with the change in cross section area. We would apply the Pascal's princile which is expressed as
F1/A1 = 2/A2
where
F1 is the force applied to the master cylinder and A1 is thecross sectional area of the master cylinder
F2 is the force created at each of the slave cylinder and A2 is the cross sectional area of slave cylinder.
In this scenario, the cork works as master cylinder and the jug as slave cylinder. From the information given,
F1 = 120
Cross sectional area of cork is
A1 = πr1^2
where r1 is the radius of the cork
Given that diameter of cork = 1.8,
radius = diameter/2 = 1.8/2
r1 = 0.9
A1 = π * 0.9^2 = 0.81π
Cross sectional area of bottle, A2 = πr2^2
where r2 is the radius of the bottom of the jug.
Given that diameter of the bottom of the jug = 18,
r2 = 18/2 = 9
A2 = π * 9^2 = 81π
From the first equation.
F2 = A2F1/A1
By substituting the given values, we have
F2 = 81π * 120/ 0.81π
F2 = 12000 N
Extra force = F2 - F1 = 12000 - 120
Extra force = 11880 N
The extra force against the bottom is 11880 N