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Zorluk: KolayPascal's Principle and Hydraulics

A hydraulic press is used to stamp metal parts. The system features an input piston with a cross-sectional area of 5 cm25 \text{ cm}^2 and an output piston with a cross-sectional area of 50 cm250 \text{ cm}^2. If a worker applies a downward force of 20 N20 \text{ N} to the input piston, what is the resulting upward force exerted by the output piston?

  1. A
    2 N2 \text{ N}
  2. B
    100 N100 \text{ N}
  3. 200 N200 \text{ N}Cevap
  4. D
    1000 N1000 \text{ N}

Cevap

The resulting upward force is 200 N200 \text{ N}.
In a closed hydraulic system, pressure is distributed equally throughout the fluid. Because the output piston's area (50 cm250 \text{ cm}^2) is 10 times larger than the input piston's area (5 cm25 \text{ cm}^2), it produces 10 times the force. Therefore, a 20 N20 \text{ N} input force is multiplied by 10, resulting in a 200 N200 \text{ N} output force.

Adım Adım Çözüm

1
Identify the given values from the problem description.
Input Force = 20 N20 \text{ N}, Input Area = 5 cm25 \text{ cm}^2, Output Area = 50 cm250 \text{ cm}^2.
These are the necessary parameters to apply Pascal's Principle.
2
Calculate the area ratio, which represents the mechanical advantage, between the output and input pistons.
Area Ratio = 50/5=1050 / 5 = 10.
The mechanical advantage in a hydraulic system is directly proportional to the ratio of the piston areas.
3
Multiply the input force by the mechanical advantage to find the final output force.
Output Force = 20×10=200 N20 \times 10 = 200 \text{ N}.
Because pressure is transmitted equally, the force is multiplied by the same factor as the area.

Anahtar Kavram

Pascal's Principle and Hydraulic Mechanical Advantage
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Pascal's Principle and Hydraulics

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