There are two round tables in the physics classroom: one with the radius of 50 cm the other with a radius of 150 cm. What is the relationship between the two forces applied on the tabletops by the atmospheric pressure?

Question

BlackTom AI · Accepted Answer

Take a moment to parse the situation: atmospheric pressure acts uniformly over each tabletop, so the total force from the air on a tabletop is pressure times its area. Since both tables are flat horizontal surfaces, the relevant quantity is their cross-sectional area, which scales with the square of the radius.

Option 1: F1/F2 = 9/1. This would imply the smaller table experiences nine times the force of the larger one. However, because areas scale with radius squared, the larger table’s area is (150/50)^2 = 3^2 = 9 times the smaller table’s area, so the larger table should experience nine times the force, not the smaller one. This option reverses the expected ratio and is incorrect.

Option 2: F1/F2 = 1/3. A ratio of 1/3 would suggest only a modest difference in forces, inconsistent with area scaling for radii differing by a factor of 3. Since area scales with r^2, the ratio should be 1:9, not 1:3. This option misapplies the area relationship and is incorrect.

Option 3: F1/F2 = 3/1. This would mean the smaller table experiences three times the force of the larger table. Again, with identical pressure and area proportional to r^2, the larger radius yields a larger area by a factor of 9, not 3. This option miscalculates the area ratio and is incorrect.

Option 4: F1/F2 = 1/9. This corresponds to the area ratio A1:A2 = (π(50 cm)^2) : (π(150 cm)^2) = 50^2 : 150^2 = 2500 : 22500 = 1 : 9. Since pressure is the same on both surfaces, the forces are proportional to area, so F1:F2 = 1:9, i.e., F1/F2 = 1/9. This option aligns with the correct area scaling and is consistent with the physics of the problem.

In summary, the reasoning relies on uniform atmospheric pressure and the fact that the force is pressure times area, with area scaling as the square of the radius. Therefore, the larger table experiences nine times the force of the smaller table, yielding a ratio of 1/9 for F1/F2 when F1 is the small-table force and F2 is the large-table force.

There are two round tables in the physics classroom: one with the radius of 50 cm the other with a radius of 150 cm. What is the relationship between the two forces applied on the tabletops by the atmospheric pressure? 单项选择题

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