The hydraulic oil in a car lift has a density of 8.29 x 10 2 kg/m 3 . The weight
ID: 2012950 • Letter: T
Question
The hydraulic oil in a car lift has a density of 8.29 x 102 kg/m3. The weight of the input piston is negligible. The radii of the input piston and output plunger are 5.38 x 10-3 m and 0.136 m, respectively. What input force F is needed to support the 24800-N combined weight of a car and the output plunger, when (a) the bottom surfaces of the piston and plunger are at the same level, and (b) the bottom surface of the output plunger is 1.40 m above that of the input plunger?
(a) Number 38.8 Units NExplanation / Answer
weight Fout = 24800 Nradii of the output piston rout = 0.136 m
radii of the input piston rin = 5.38 x 10-3 m we know that , force F = pressure*area therefore , F A from this equation , F1/F2 = A1/A2
a) from above relation , Fin / Fout = Ain / Aout
Fin = [Fout](rin / rout)2
= [24800 N]( 5.38 x 10-3 m / 0.136 m)2
= 38.80 N
b) the bottom surface of the output plunger rout = 1.4 m
Fin / Fout = Ain / Aout
Fin = [Fout](rin / rout)2
= [24800 N]( 5.38 x 10-3 m / 1.4 m)2
= 0.366 N
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