Question

ДАЮ 100 БАЛЛОВ, ОБЪЯСНИТЕ ВСЁ ПОДРОБНЕЕ 3 К коромыслу весов подвешены два цилиндра одинакового объема: железный и алюминевый. С помощью дополнительного груза весы уравновешены. Нарушится ли равновесие весов, если оба цилиндра погрузить в воду? Ответ обознуйте.

Answer 1

Ответ:

По формуле сила Архимеда $(F_{A} = \rho g V)$, зависит только от объема тела и плотности жидкости в которую погружают цилиндры, а также от ускорения свободного падения (но оно неизменно). Если предположить, что груз, который уравновешивает цилиндры не имеет объема (например лежит внутри цилиндра, то на цилиндры будет действовать одинаковая сила Архимеда, так как согласно формуле она зависит лишь от объема тела и плотности жидкости в которую погружают тело (g также одинаковое; согласно условию, цилиндры имеют одинаковый объем и погружают в жидкость с одинаковой плотностью), то есть весы останутся в равновесии.

Answer 2

The Principle of Buoyancy and Archimedes' Principle

When two cylinders of equal volume, one made of iron and the other made of aluminum, are suspended from a balance, the balance will be in equilibrium when an additional weight is added. The question is whether this equilibrium will be disrupted if both cylinders are submerged in water.

To answer this question, we need to understand the principle of buoyancy and Archimedes' principle. According to Archimedes' principle, an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This buoyant force acts in the opposite direction to the force of gravity.

The Effect of Submerging the Cylinders in Water

When both cylinders are submerged in water, they will displace a certain volume of water equal to their own volume. The buoyant force acting on each cylinder will be equal to the weight of the water displaced by that cylinder. Since both cylinders have the same volume, they will displace the same amount of water and experience the same buoyant force.

If the weight of the water displaced by each cylinder is equal to the weight of the cylinder itself, then the buoyant force will exactly balance the weight of the cylinder. This means that the equilibrium of the balance will not be disrupted when both cylinders are submerged in water.

In other words, the balance will remain in equilibrium even when both cylinders are submerged in water. The additional weight needed to balance the cylinders on the balance will still be necessary, and the equilibrium will not be affected.

Conclusion

In summary, when two cylinders of equal volume, one made of iron and the other made of aluminum, are suspended from a balance and an additional weight is added to achieve equilibrium, the equilibrium will not be disrupted if both cylinders are submerged in water. The balance will remain in equilibrium, and the additional weight will still be necessary to balance the cylinders.

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