Solution to problem 13.7.7 from the collection of Kepe O.E.

13.7.7 The speed of movement of a vessel filled with water must change with acceleration so that the free surface of the water inside the vessel becomes parallel to an inclined plane having an angle of inclination ?=20°. Determine the amount of acceleration required. (Answer 3.36)

It is required to determine the acceleration of motion of a vessel filled with water, at which the free surface of the water inside the vessel becomes parallel to the inclined plane with an angle of inclination ?=20°. The answer to the problem is 3.36.

To solve the problem it is necessary to use Archimedes' law and the balance of forces equation. As a result of calculations, it can be obtained that the acceleration should be equal to 3.36 m/s².

Thus, in order for the free surface of water inside the vessel to become parallel to the inclined plane of the angle of inclination ?=20°, it is necessary to ensure an acceleration of the vessel movement equal to 3.36 m/s².

Problem 13.7.7 from the collection of Kepe O.?. consists in determining the acceleration of movement of a vessel filled with water, at which the free surface of the water inside the vessel becomes parallel to the inclined plane of the angle of inclination ? = 20°. To solve this problem it is necessary to use Archimedes' law and the balance of forces equation. As a result of calculations, it can be obtained that the acceleration should be equal to 3.36 m/s². Thus, in order for the free surface of water inside the vessel to become parallel to the inclined plane of the angle of inclination ?=20°, it is necessary to ensure an acceleration of the vessel movement equal to 3.36 m/s². The answer to the problem is 3.36.

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Solution to problem 13.7.7 from the collection of Kepe O.?. requires determining the acceleration a required for the free surface of the water in the vessel to become parallel to the inclined plane, at an angle of 20 degrees.

To solve this problem it is necessary to use physical laws, in particular, the law of conservation of energy. The angle of inclination of the plane and the height of the water in the vessel make it possible to determine the potential energy of the system. The change in the potential energy of the system when the acceleration a changes is equal to the work done by gravity.

In order for the free surface of water in the vessel to become parallel to the inclined plane, at an inclination angle of 20 degrees, it is necessary that the force of gravity acting on the liquid be compensated by the force of inertia acting on the vessel. From the equality of these forces, we can express the acceleration a necessary to achieve the required position of the free surface of the water.

After applying the appropriate formulas and calculations, we find that the required acceleration a is 3.36 m/s². The answer to the problem is exactly this number.

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