The 70 kg student in figure p14. 43 balances a 1200 kg elephant on a hydraulic lift. What is the diameter of the piston the student is standing on?.

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22-11-2022
Physics

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The 70 kg student in figure p14. 43 balances a 1200 kg elephant on a hydraulic lift. What is the diameter of the piston the student is standing on?.

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triptivt3 triptivt3 · Answer 1 · 2022-11-27T00:39:04-05:00

The piston the student is standing on has a 0.22-times larger diameter than the piston the elephant stands on.

What is mechanical advantage of a hydraulic lift?

Pascal's law is shown via the hydraulic system.
In doing so, we are able to use a modest force on the small piston to generate a bigger force on the huge piston.
At each piston, the ratio between the force and the area must be the same.
The three practical tools that make use of Pascal's law are hydraulic presses, hydraulic lifts, and hydraulic brakes.

Given parameters:

Mass of the student: m = 70 kg.

Mass of the elephant: M = 1200 kg.

Let the diameters of the piston the student is standing on and the piston the elephant is standing on are respectively d and D.

Using Pascal's law , we can write,

Force applied by the student's weight ÷ area of the piston the student is standing on = Force applied by the elephant's weight ÷ area of the piston the elephant is standing on.

⇒ 70 kg × g / π d² = 1200 kg × g / π D²

⇒ 1400 d² = 70 D²

⇒ d= 0.22D.

Hence, The piston the student is standing on has a diameter that is 0.22 times larger than the piston the elephant is standing on.

Learn more about mechanical advantage here:

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