Answer to Part A: 65.56N The hydraulic oil in a car lift has a density of 8.09 x

Question

Answer to Part A: 65.56N

The hydraulic oil in a car lift has a density of 8.09 x 102 kg/m3. The weight of the input piston is negligible. The radii of the input piston and output plunger are 5.63 x 10-3 m and 0.118 m, respectively. What input force F is needed to support the 28800-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 1.30 m above that of the input plunger?

Explanation / Answer

The out put force is weigth of the car Fout = 28800N

In put radius of the piston rin = 5.63*10^-3m

the output radius of the plunger rout= 0.118m

The input force frm partA is Fin = 65.56N

the heigth difference between input and output plunger h = 1.30m

The input pressure = output pressure + gh

Fin/Ain = Fout/Aout + gh

Fin = (Ain/Aout) Fout + gh Ain

     = (rin^2 /rout^2) (Fout) + gh(rin^2)

    = (5.63*10^-3/0.118)^2 (28800) + (809)(9.8)(1.3)(3.14)(5.63*10^-3)^2

    = 65.56 + 1.025

     = 66.585 N

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