QuestionAugust 19, 2025

15. To lift an object with a weight of 21,000 N how much force is needed on a piston with the area of 0.060m^2 if the platform being lifted has an area of 3.0m^2

15. To lift an object with a weight of 21,000 N how much force is needed on a piston with the area of 0.060m^2 if the platform being lifted has an area of 3.0m^2
15. To lift an object with a weight of 21,000 N how much force is needed on a piston with the area of 0.060m^2 if the platform being lifted has an area of 3.0m^2

Solution
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Answer

420 N Explanation 1. Apply Pascal's Principle According to Pascal's principle, the pressure applied on a confined fluid is transmitted undiminished throughout the fluid. Thus, P_1 = P_2 where P = \frac{F}{A}. 2. Calculate Pressure on Platform The pressure exerted by the weight of the object is P_2 = \frac{21,000 \, \text{N}}{3.0 \, m^2} = 7,000 \, \text{Pa}. 3. Calculate Force on Piston Using P_1 = P_2, we have \frac{F_1}{0.060 \, m^2} = 7,000 \, \text{Pa}. Solving for F_1, F_1 = 7,000 \, \text{Pa} \times 0.060 \, m^2 = 420 \, \text{N}.

Explanation

1. Apply Pascal's Principle<br /> According to Pascal's principle, the pressure applied on a confined fluid is transmitted undiminished throughout the fluid. Thus, $P_1 = P_2$ where $P = \frac{F}{A}$.<br /><br />2. Calculate Pressure on Platform<br /> The pressure exerted by the weight of the object is $P_2 = \frac{21,000 \, \text{N}}{3.0 \, m^2} = 7,000 \, \text{Pa}$.<br /><br />3. Calculate Force on Piston<br /> Using $P_1 = P_2$, we have $\frac{F_1}{0.060 \, m^2} = 7,000 \, \text{Pa}$. Solving for $F_1$, $F_1 = 7,000 \, \text{Pa} \times 0.060 \, m^2 = 420 \, \text{N}$.
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