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42. Pistons are fitted to two cylindrical chambers connected through a horizontal tune to form a hydraulic system. The piston chambers and the connecting tube are Filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A1and A2, respectively. A force Ffis excited on piston 1. Rank the resultant force F2on piston 2 that results from the combinations of F1 A 1 and A2 given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking.
(a) F1= 2.0 N; A1 = 0.5 m2; and A2= 1.0 m2
(b) Fl= 1.0 N; A1= 0.5 m2; and A2 = 0.25 m2.
(c) F1= 1.0 N; A1= 1.0 m2; and A2= 2.0 m2.
(d) F1 = 2.0 N; A1= 0.25 m2; and A2 = 1.0 m2.
(e) F1 = 2.0 N; A1= 0.25 m2; and A2 = 0.5 m2
(f) F1 = 1.0 N; A1 = 1.0 m2; and A2= 0.5 m2.
Rank the resultant force F2 on piston 2 that results from the combinations of F1, A1, and A2 given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking.
Answer to Problem 42Q
The order of force
Explanation of Solution
Given:
Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a hydraulic system. The piston chambers and the connecting tube are filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A1 and A2, respectively. A force F1 is exerted on piston 1.
(a)F1 = 2.0 N; A1 = 0.5 m2 ; and A2 = 1.0 m2
(b)F1 = 1.0 N; A1 = 0.5 m2 ; and A2 = 0.25 m2
(c)F1 = 1.0 N; A1 = 1.0 m2 ; and A2 = 2.0 m2
(d)F1 = 2.0 N; A1 = 0.25 m2 ; and A2 = 1.0 m2
(e)F1 = 2.0 N; A1 = 0.25 m2 ; and A2 = 0.5 m2
(f)F1 = 1.0 N; A1 = 1.0 m2 ; and A2 = 0.5 m2.
Formula used:
The expression for pressure is given as
Since the pressure is the same
Using the above expression, we can find the resultant force
Calculation:
(a)
(b)
(c)
(d)
(e)
(f)
The order of force
Conclusion:
The order of force
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