Destroy a wine barrel
Question
Solution
Short
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\(\LaTeX\)
Amédée Guillemin, , 1872, illustration, The forces of nature: a popular introduction to the study of physical phenomena p. 69
<Wikipedia> (retrieved on November 28, 2022)
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The following quantities appear in the problem:
Kraft \(F\) / Druck \(p\) / Fläche \(A\) / Ortsfaktor \(g\) / Höhe \(h\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(p = \dfrac{F}{A} \quad \) \(A = \pi r^2 \quad \) \(p = \varrho g h \quad \)
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Exercise:
In the th century french physicist Blaise Pascal claimed that he could destroy a full wine barrel with a few glasses of wine. A long tube rO inner radius was inserted o a water-filled wine barrel RO lid radius and water was filled o the long tube until the barrel burst. This happened at a filling height of hO. By what factor is the force on the lid bigger than the weight of the liquid in the small tube?
Solution:
Geg r rO r R RO R h h GesfactorN % The pressure of the water column is NewQtyrwkgpmk SolQtyprwX*ncgn*hXPa al p rho g h rw ncg h p. This pressure acts on the lid its circular surface is SolQtyApi*RX^metersquared al A pi R^ pi qtyR^ A The force acting on the circular lid is then SolQtyFpX*AXN al F p A rho g h pi R^ pirho ghR^ p A F. In the tube it has SolQtyVpi*rX^*hXcubicmeter V pi r^ h pi qtyr^ h V water with a mass of SolQtymrwX*VXkg m rho V rw V m and SolQtyFgmX*ncgnN sscFG mg m ncg Fg in weight. The force acting on the lid is therefore SolQtyNFX/FgX N fracFsscFG N times bigger than the weight of the water in the small lid. N N
In the th century french physicist Blaise Pascal claimed that he could destroy a full wine barrel with a few glasses of wine. A long tube rO inner radius was inserted o a water-filled wine barrel RO lid radius and water was filled o the long tube until the barrel burst. This happened at a filling height of hO. By what factor is the force on the lid bigger than the weight of the liquid in the small tube?
Solution:
Geg r rO r R RO R h h GesfactorN % The pressure of the water column is NewQtyrwkgpmk SolQtyprwX*ncgn*hXPa al p rho g h rw ncg h p. This pressure acts on the lid its circular surface is SolQtyApi*RX^metersquared al A pi R^ pi qtyR^ A The force acting on the circular lid is then SolQtyFpX*AXN al F p A rho g h pi R^ pirho ghR^ p A F. In the tube it has SolQtyVpi*rX^*hXcubicmeter V pi r^ h pi qtyr^ h V water with a mass of SolQtymrwX*VXkg m rho V rw V m and SolQtyFgmX*ncgnN sscFG mg m ncg Fg in weight. The force acting on the lid is therefore SolQtyNFX/FgX N fracFsscFG N times bigger than the weight of the water in the small lid. N N