Question

10 Тело подвесили на пружине СРОЧНО ПОМОГИТЕ ПОЖАЛУЙСТА ДАМ ВСЕ БАЛЛЫ динамометра. Вес тела оказался равен 26 кН. Не снимая тела с пружины, его целиком погрузили в воду. При этом показания динамометра уменьшились до 16 кН. Каков объём тела? Плотность воды равна 1000 кг/м3. Нарисуйте силы, действующие на тело в воздухе и воде.

Answer 1

Problem Analysis

In this problem, a body is suspended on a spring and its weight is measured using a dynamometer. The body is then fully submerged in water, causing the reading on the dynamometer to decrease. We need to determine the volume of the body, given that its weight is 26 kN in air and 16 kN in water. The density of water is given as 1000 kg/m^3. We also need to draw the forces acting on the body in air and water.

Solution

To solve this problem, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Let's break down the solution into steps:

1. Calculate the weight of the body in air and water: - The weight of the body in air is given as 26 kN. - The weight of the body in water is given as 16 kN.

2. Calculate the difference in weight between air and water: - The difference in weight between air and water is equal to the buoyant force acting on the body when it is submerged in water. - This difference can be calculated by subtracting the weight of the body in water from the weight of the body in air.

3. Calculate the volume of the body: - The volume of the body can be calculated using the formula: volume = buoyant force / (density of water * acceleration due to gravity). - The buoyant force is equal to the difference in weight between air and water. - The density of water is given as 1000 kg/m^3. - The acceleration due to gravity is approximately 9.8 m/s^2.

4. Draw the forces acting on the body in air and water: - In air, the only force acting on the body is its weight, which is directed downwards. - In water, the body experiences an upward buoyant force, which is equal to the weight of the water displaced by the body, and a downward force due to its weight.

Let's calculate the volume of the body and draw the forces acting on it.

Calculation

1. Calculate the difference in weight between air and water: - Difference in weight = Weight in air - Weight in water - Difference in weight = 26 kN - 16 kN - Difference in weight = 10 kN

2. Calculate the volume of the body: - Volume = Difference in weight / (Density of water * Acceleration due to gravity) - Volume = 10 kN / (1000 kg/m^3 * 9.8 m/s^2) - Volume ≈ 1.02 m^3

Forces Acting on the Body

In air: - Weight: The weight of the body acts downwards.

In water: - Buoyant force: The buoyant force acts upwards and is equal to the weight of the water displaced by the body. - Weight: The weight of the body acts downwards.

Please note that the forces are not drawn to scale.


Conclusion

The volume of the body is approximately 1.02 m^3. The forces acting on the body in air are its weight acting downwards, while in water, the body experiences an upward buoyant force and a downward force due to its weight.