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Calculate the pressure exerted by the mercury column.

Physics

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Answer

10,180 kPa\text{10,180 kPa}

Step-by-step solution

3 steps

9.

  1. Calculate the pressure exerted by the mercury column.

    The pressure due to a column of fluid is given by the formula P=ρghP = \rho g h.
    Given:
    Density of mercury (ρ\rho) = 14,000 kg/m314,000 \text{ kg/m}^3
    Acceleration due to gravity (gg) = 10 N/kg=10 m/s210 \text{ N/kg} = 10 \text{ m/s}^2
    Difference in height (hh) = 72 m72 \text{ m}

    Pcolumn=ρghP_{column} = \rho g h Pcolumn=14,000 kg/m3×10 m/s2×72 mP_{column} = 14,000 \text{ kg/m}^3 \times 10 \text{ m/s}^2 \times 72 \text{ m} Pcolumn=10,080,000 PaP_{column} = 10,080,000 \text{ Pa}
  2. Convert the pressure to kilopascals (kPa).

    1 kPa=1000 Pa1 \text{ kPa} = 1000 \text{ Pa} Pcolumn=10,080,0001000 kPaP_{column} = \frac{10,080,000}{1000} \text{ kPa} Pcolumn=10,080 kPaP_{column} = 10,080 \text{ kPa}
  3. Determine the pressure of the gas supply.

    From the diagram, the mercury level in the arm connected to the gas supply (left side) is lower than the mercury level in the arm open to the atmosphere (right side). This indicates that the pressure of the gas supply is greater than the atmospheric pressure.

    Pgas=Patm+PcolumnP_{gas} = P_{atm} + P_{column}

    Given atmospheric pressure (PatmP_{atm}) = 100 kPa100 \text{ kPa}.

    Pgas=100 kPa+10,080 kPaP_{gas} = 100 \text{ kPa} + 10,080 \text{ kPa} Pgas=10,180 kPaP_{gas} = 10,180 \text{ kPa}

    The pressure of the gas supply is 10,180 kPa\boxed{\text{10,180 kPa}}.

    10.

    • Effect on stability: His stability will increase.
    • Explanation: Spreading his feet further apart increases the base area (or base of support) of the athlete. For an object to be stable, its center of gravity must fall within its base of support. A larger base area means the center of gravity can shift a greater distance horizontally before it falls outside the base, making the athlete more stable and less likely to topple over, especially when lifting heavy weights.
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