Question

A hydraulic machine is used to providea mechanical advantage; m₁ = 0: 025 kg, m₂ = 7500 kg.

a) Derive an algebraic equation for themechanical advantage.
b) Calculate D₂ (given that D

Answer 1

To solve for the mechanical advantage, use the equation MA = m2/m1. To calculate D2, substitute values into the equation D2 = D1 * √(m2/m1).

Step-by-step explanation:

To derive the algebraic equation for mechanical advantage in a hydraulic machine, we can use the formula MA = Fout/Fin. In this case, the force exerted by the smaller piston (Fin) is equal to the force exerted by the larger piston (Fout). So, we have MA = Fout/Fin = (m2 * g)/(m1 * g). Simplifying this equation further, we get MA = m2/m1.

To calculate D2, we need to know the diameter of the smaller piston (D1) and the diameter of the larger piston (D2). The formula for calculating the area of a circle is A = πr2. Therefore, the area of the smaller piston is A1 = (πD12)/4 and the area of the larger piston is A2 = (πD22)/4. Since pressure is defined as force per unit area, we know that Pin = Fin/A1 and Pout = Fout/A2. Since the force exerted by the smaller piston is equal to the force exerted by the larger piston, we can equate Pin = Pout. This gives us m1*g/A1 = m2*g/A2. Simplifying this equation further, we get A2/A1 = m2/m1. We know that A2 = πD22/4 and A1 = πD12/4, so we can substitute these values into the equation to get D2 = D1 * √(m2/m1).

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