Question

Задача 1 Бутылка в море Оказавшись на необитаемом острове посреди океана юный физик решил отправить сообщение о бедстии. Найдя стеклянную бутыль, массой 360г. он заметил, что в отдаленном приближении бутылка состоит из двух цилиндров диаметрами 30 и 80 мм. По высоте горлышко в два раза меньше большего цилиндра. Какой объём песка физик должен насыпать в бутылку, чтобы она была погружена в воду ровно наполовину, ведь отправив таким образом сообщение его должны как можно лучше заместить? Считать, что лист бумаги с сообщением SOS ничего не весит, а вот глиняная пробка весит 30г. Плотность воды мирового океана 1020кг/м³, а высота бутылки 240мм.

Answer 1

To solve this problem, we need to calculate the volume of sand that the physicist should pour into the bottle in order for it to be submerged halfway in the water. Let's break down the problem step by step.

Given Information:

- Mass of the glass bottle: 360g - The bottle consists of two cylinders with diameters of 30mm and 80mm. - The height of the neck is half the height of the larger cylinder. - The height of the bottle is 240mm. - The weight of the clay plug is 30g. - The density of seawater is 1020kg/m³.

Calculating the Volume of the Bottle:

To calculate the volume of the bottle, we need to find the sum of the volumes of the two cylinders.

The volume of a cylinder can be calculated using the formula: V = πr²h, where r is the radius and h is the height.

For the larger cylinder: - Radius (r₁) = diameter (d₁) / 2 = 80mm / 2 = 40mm = 0.04m - Height (h₁) = 240mm = 0.24m

For the smaller cylinder (neck): - Radius (r₂) = diameter (d₂) / 2 = 30mm / 2 = 15mm = 0.015m - Height (h₂) = h₁ / 2 = 0.24m / 2 = 0.12m

Now we can calculate the volume of the bottle: - Volume of the larger cylinder (V₁) = π(0.04m)²(0.24m) - Volume of the smaller cylinder (V₂) = π(0.015m)²(0.12m) - Total volume of the bottle (V_total) = V₁ + V₂

Calculating the Volume of Water Displaced:

To calculate the volume of water displaced when the bottle is submerged halfway, we need to find half of the total volume of the bottle.

- Volume of water displaced (V_water) = V_total / 2

Calculating the Volume of Sand:

To calculate the volume of sand that needs to be poured into the bottle, we subtract the volume of the clay plug from the volume of water displaced.

- Volume of clay plug = mass of clay plug / density of seawater = 30g / 1020kg/m³ - Volume of sand (V_sand) = V_water - Volume of clay plug

Now we can calculate the volume of sand.

Answer:

The physicist should pour V_sand volume of sand into the bottle to submerge it halfway in the water.

Please note that I cannot perform the calculations without the actual values for the mass of the clay plug and the density of seawater. If you provide those values, I can help you calculate the volume of sand.