Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The hydraulic oil in a car lift has a density of 8.30 102 kg/m3. The weight of t

ID: 2017638 • Letter: T

Question

The hydraulic oil in a car lift has a density of 8.30 102 kg/m3. The weight of the input piston is negligible. The radii of the input piston and output plunger are 6.50 10-3 m and 0.125 m, respectively. What input force F is needed to support the 25500 N combined weight of a car and the output plunger under the following conditions?
(a) The bottom surfaces of the piston and plunger are at the same level.
1 N

(b) The bottom surface of the output plunger is 1.10 m above that of the input piston.
2 N

Explanation / Answer

weight Fout = 25500 N
radii of the output piston rout = 0.125 m
radii of the input piston rin = 6.5 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
                     = [25500 N]( 6.5 x 10-3 m / 0.125 m)2
                     = 68.95 N
b) the bottom surface of the output plunger rout = 1.1 m
  the output piston movens a smaller distance than the input piston work done = Fi * di                   = 68.95*1.1 m                    = 75.845 J F0do = Fidi Fi = F0d0/di     = (68.95 N ) / 1.1m     = 62.68 N here F0 is the force which are at same height . weight Fout = 25500 N
radii of the output piston rout = 0.125 m
radii of the input piston rin = 6.5 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
                     = [25500 N]( 6.5 x 10-3 m / 0.125 m)2
                     = 68.95 N
b) the bottom surface of the output plunger rout = 1.1 m
  the output piston movens a smaller distance than the input piston work done = Fi * di                   = 68.95*1.1 m                    = 75.845 J F0do = Fidi Fi = F0d0/di     = (68.95 N ) / 1.1m     = 62.68 N here F0 is the force which are at same height .