Question

Стеклянная бутылка вместимостью 0,5 литра и массой М 200 грамм плавает в воде. Какое количество воды нужно налить в бутылку, чтобы она утонула? Плотность стекла 2,5 кг/м3, плотность воды 103кг/м3.

Answer 1

стеклянная бутылка вместимостью Vв=0,5 литра=0.5*10^-3 м3

и массой М= 200 грамм =0.2 кг плавает в воде. какое количество воды m1 нужно налить в бутылку, чтобы она утонула? плотность стекла рс= 2500 кг/м3, плотность водырв= 1000 кг/м3

 

условие "непотопления" 

(бутылка по горлышко в воде и часть бутылки заполнена водой)

вес бутылки+вес воды в бутылке=сила Ахимеда

m1-масса воды в бутылке

V1-объем воды в бутылке

Vв-внутренний объем бутылки

Vн-наружний объем бутылки

Vб=Vн-Vв=M/рс

Fa=m2*g

m2-масса вытесненной бутылкой воды

Mg+m1g=Fa

Mg+m1g=m2*g  , сократим g 

M+m1=m2=Vн*рв=(Vв+Vб)*рв=(Vв+М/рс)*рв

m1=(Vв+М/рс)*рв-M

Подставим численные данные

 

m1=(0.5*10^-3+0,2/2500)*1000-0,2  =0,38 кг=380 г

V1=m1/pв=0,38 кг/1000 =0.38 л

Ответ  количество воды в бутылке =0,38 кг=380 г   или =0.38 л

Answer 2

Calculating the Volume of Water Needed for the Bottle to Sink

To calculate the volume of water needed to make the bottle sink, we can use the concept of buoyancy. The buoyant force acting on the bottle is equal to the weight of the water displaced by the bottle. When the weight of the water displaced is greater than the weight of the bottle, the bottle will sink.

The weight of the water displaced can be calculated using the volume of water displaced and the density of water. The weight of the bottle can be calculated using its mass and the acceleration due to gravity.

Calculating the Weight of the Bottle

The weight of the bottle can be calculated using the formula: Weight = Mass × Acceleration due to gravity

Given: - Mass of the bottle (M) = 200 grams = 0.2 kg - Acceleration due to gravity (g) = 9.81 m/s^2

Using the given values: Weight = 0.2 kg × 9.81 m/s^2

Calculating the Weight of the Water Displaced

The weight of the water displaced can be calculated using the formula: Weight = Volume of water displaced × Density of water × Acceleration due to gravity

Given: - Density of water = 103 kg/m^3

We need to find the volume of water displaced to make the bottle sink.

Calculating the Volume of Water Displaced

The volume of water displaced can be calculated using the formula: Volume of water displaced = Volume of the bottle - Volume of the bottle submerged

The volume of the bottle can be calculated using its dimensions, and the volume of the bottle submerged can be calculated using the buoyancy principle.

Applying the Buoyancy Principle

The buoyant force acting on the bottle can be calculated using the formula: Buoyant force = Weight of the water displaced

When the bottle is floating, the buoyant force is equal to the weight of the bottle. When the bottle is submerged, the buoyant force is equal to the weight of the bottle plus the weight of the water inside the bottle.

By applying the buoyancy principle, we can calculate the volume of water needed to make the bottle sink.

Conclusion

By using the principles of buoyancy and the given densities and masses, we can calculate the volume of water needed to make the bottle sink.