The radius of the output tube should be one-fourth the radius of the input tube to achieve an output force that is 16 times the input force.
How to determine what should the radius of the output tube be in order for the output force to be 16 times the input forceIn a hydraulic lever, the principle of Pascal's law applies, which states that the pressure in an enclosed fluid is transmitted equally in all directions. Based on this principle, we can calculate the required radius of the output tube to achieve the desired output force.
Let's denote the radius of the input tube as r₁ and the radius of the output tube as r₂. According to the principle of Pascal's law, the pressure in the fluid is the same in both tubes.
We can use the formula for pressure in a fluid:
Pressure = Force / Area
The force exerted on the fluid in the input tube is the input force (F₁), and the force exerted on the fluid in the output tube is the output force (F₂). Since the pressure is the same, we can equate the pressure in the input tube to the pressure in the output tube:
F₁ / (π * r₁²) = F₂ / (π * r₂²)
Simplifying the equation:
F₂ = 16 * F₁
Now we can substitute this relationship into the equation:
F₁ / (π * r₁²) = (16 * F₁) / (π * r₂²)
Simplifying further:
r₂² = r₁² / 16
Taking the square root of both sides:
r₂ = r₁ / 4
Therefore, the radius of the output tube should be one-fourth the radius of the input tube to achieve an output force that is 16 times the input force.
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