The problem I need figured out is from the Physlet Physics book by Wolfgang Chri

Question

The problem I need figured out is from the Physlet Physics book by Wolfgang Christian & Mario Belloni Problem 14.1 page 123. You will also need the interactive CD that comes with the book to see the diagram pictured below in order to get the diameter of the circular lids via a plus sign that shows the x coordinate position when moved over the graph area. (position is given in centimeters).

 

(a.) I need to know what force is required on the left side to support the 40-kg mass?

 

(b.) If the mass is lifted up 1 cm, how far down does the fluid on the left need to be pushed?

 

Explanation / Answer

From the given figure , in graph each cell having an area = 1*10^-3 m^2 The radius of the right side circular lid is r2 = 15*10^-3 m /2 = 7.5*10^-3 m The radius of the left side circular side lid is r1 = 1*10^-3 m The mass m = 40kg Then from the pascal law                      F1 = F2(A1/A2)                           = (40 kg *9.8 m/s^2)[ (1*10^-3 m)^2 / (7.5*10^-3 m)^2]                       = 6.97 N (b) When the mass lifted up by h2 = 1cm then since the liquid is incompressible so              h1 A1 = h2 A2 then             h1 = h2 A2 / A1                  =(1.0cm )[ (7.5*10^-3 m)^2 / (1*10^-3 m)^2]                  = 56.25 cm                 

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