This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Another day — let's solve it. Step 1: Convert all given heights to meters. The atmospheric pressure is given as 75 cmHg. h_atm = 75 cm = 0.75 m The height of the water column is 68 cm. h_water = 68 cm = 0.68 m The difference in the mercury levels in the U-tube is 30 cm. h_Hg\_diff = 30 cm = 0.30 m Step 2: Calculate the atmospheric pressure (P_atm) in Pascals. The formula for pressure due to a fluid column is P = g h. Given density of mercury (_Hg) = 13600 kg/m^3. Acceleration due to gravity (g) = 9.8 m/s^2. P_atm = _Hg g h_atm P_atm = 13600 kg/m^3 × 9.8 m/s^2 × 0.75 m P_atm = 99960 Pa Step 3: Calculate the pressure due to the water column (P_water). Density of water (_water) = 1000 kg/m^3. P_water = _water g h_water P_water = 1000 kg/m^3 × 9.8 m/s^2 × 0.68 m P_water = 6664 Pa Step 4: Calculate the pressure due to the mercury column difference (P_Hg\_diff). P_Hg\_diff = _Hg g h_Hg\_diff P_Hg\_diff = 13600 kg/m^3 × 9.8 m/s^2 × 0.30 m P_Hg\_diff = 39984 Pa Step 5: Determine the pressure of the trapped air (P_air). By balancing the pressure at the horizontal level of the lower mercury surface (indicated by the dashed line): The pressure on the left side (open to atmosphere) is P_atm. The pressure on the right side (containing trapped air, water, and mercury above the dashed line) is the sum of the trapped air pressure, the pressure due to the water column, and the pressure due to the mercury column difference. P_atm = P_air + P_water + P_Hg\_diff Rearrange to solve for P_air: P_air = P_atm - P_water - P_Hg\_diff P_air = 99960 Pa - 6664 Pa - 39984 Pa P_air = 53312 Pa The pressure of the trapped air is: 53312 Pa Last free one today — make it count tomorrow, or type /upgrade for unlimited.