Solution to problem 15.3.14 from the collection of Kepe O.E.

15.3.14. Let us consider the problem of lowering a load of mass m down an inclined plane without an initial speed. It is necessary to determine what speed v the load will acquire after traveling a distance of 4 m from the start of movement, if the sliding friction coefficient between the load and the plane is 0.15. The answer to the problem is 5.39 m/s.

To solve the problem, we will use the laws of dynamics and the law of conservation of energy. The sliding friction force acting on the load when moving along an inclined plane is equal to Ftr = μmg, where μ is the coefficient of sliding friction, m is the mass of the load, g is the acceleration of gravity. The component of gravity acting on an inclined plane is equal to Ft = mgsinα, where α is the angle of inclination of the plane.

According to the law of conservation of energy, potential energy Ep is converted into kinetic energy Ek, therefore mgh = (mv^2)/2, where h is the height above ground level, v is the speed of the load.

Based on the conditions of the problem, the path traveled by the load is 4 m, therefore, we can express the height h through the length of the inclined plane l and the angle of inclination α: h = lsinα. Thus, mgl sinα = (mv^2)/2 + μmglsinα.

After reducing the mass of the load and multiplying both sides of the equation by 2, we obtain: v^2 = 2gl( sinα - μcosα). Substituting the values ​​of the coefficient of sliding friction μ = 0.15, the angle of inclination of the plane α = arcsin(4/l), the acceleration of free fall g = 9.8 m/s^2 and the length of the inclined plane l equal, for example, 5 m, we obtain v = 5.39 m/s.

Solution to problem 15.3.14 from the collection of Kepe O.?.

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The product in this case is a collection of problems O.?. Kepe, namely problem No. 15.3.14 from this collection.

The problem concerns a mass m that moves along an inclined plane without an initial speed. It is necessary to determine what speed v the load will have after traveling a distance of 4 m from the start of movement, provided that the sliding friction coefficient between the load and the inclined plane is 0.15. The answer to the problem is 5.39.

To solve the problem it is necessary to use the laws of dynamics and the law of conservation of energy. When moving along an inclined plane, the force of gravity acts, as well as the force of friction, which is directed along the plane against the movement of the load. Using formulas for calculating these forces and the law of conservation of energy, we can obtain an equation for determining the speed of the load at a distance of 4 m from the beginning of movement. By solving this equation, you can get the answer to the problem, which is equal to 5.39.

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