To determine the pressure exerted by the force applied at point A, the pressure on point B by the oil, and the force produced on B compressing the bale, we can use Pascal's principle and the formulas for pressure.
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Pressure Exerted on the Oil by the Force Applied at A (P₁):
\[ P_{1} = \frac{F_{A}}{A_{A}} \] where:
- \( P_{1} \) = pressure at A
- \( F_{A} \) = force applied at A (in newtons)
- \( A_{A} = 0.002 , \text{m}^2 \) = cross-sectional area at A.
To find \( P_{1} \), we need the value of \( F_{A} \).
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Pressure Exerted on B by the Oil (P₂):
By Pascal's principle, the pressure is the same throughout the incompressible fluid. Therefore, the pressure at B (P₂) will be equal to the pressure at A (P₁):
\[ P_{2} = P_{1} \]
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Force Produced on B Compressing the Bale (F₁):
To find the force exerted on B (F₁), we can use the relationship:
\[ P_{2} = \frac{F_{B}}{A_{B}} \] where:
- \( F_{B} \) = force exerted on B
- \( A_{B} = 0.30 , \text{m}^2 \) = cross-sectional area at B.
Rearranging gives us:
\[ F_{B} = P_{2} \cdot A_{B} \]
Example Calculation
Assuming you have a force \( F_A \) of, say, 100 N applied at point A, you can use these formulas:
- Calculate Pressure at A (P₁):
\[ P_{1} = \frac{100 , \text{N}}{0.002 , \text{m}^2} = 50000 , \text{Pa} \text{ or } 50 , \text{kPa} \]
- Pressure at B (P₂):
\[ P_{2} = P_{1} = 50000 , \text{Pa} \]
- Force at B (F₁):
\[ F_{B} = P_{2} \cdot A_{B} = 50000 , \text{Pa} \cdot 0.30 , \text{m}^2 = 15000 , \text{N} \]
Conclusions
- The pressure exerted on the oil by the force applied at A is 50000 Pa.
- The pressure on B by the oil is also 50000 Pa.
- The force produced on B compressing the bale is 15000 N.
You can substitute any value of \( F_A \) to calculate specific scenarios.