Solution to problem 13.4.24 from the collection of Kepe O.E.

13.4.24 Let’s take a load weighing 9 kg, hang it from a spring with a stiffness coefficient of 90 N/m and let it go into free vertical vibrations with an amplitude of 0.1 m, starting from a position of static equilibrium. It is necessary to determine the initial speed of the load. Answer: 0.316.

Solution to problem 13.4.24 from the collection of Kepe O.?.

This digital product is a solution to problem 13.4.24 from the collection of Kepe O.?. in a convenient format. The solution is completed by a professional teacher and presented in an understandable manner.

The problem is to determine the initial speed of a load weighing 9 kg, suspended from a spring with a stiffness coefficient of 90 N/m, which performs free vertical vibrations with an amplitude of 0.1 m. Solving this problem will help you better understand the material associated with vibrations and waves, and also prepare for exams and testing.

Buy the digital product "Solution to problem 13.4.24 from the collection of Kepe O.?." and get access to a high-quality and understandable solution to the problem.

Digital product "Solution to problem 13.4.24 from the collection of Kepe O.?." is a professionally executed solution to the problem of determining the initial speed of a load weighing 9 kg, suspended from a spring with a stiffness coefficient of 90 N/m and performing free vertical oscillations with an amplitude of 0.1 m. The solution is presented in a convenient format and will help you better understand material related to oscillations and waves, as well as prepare for exams and testing. By purchasing this digital product, you will get access to a high-quality and understandable solution to the problem, performed by a professional teacher. The answer to the problem is 0.316.

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Solution to problem 13.4.24 from the collection of Kepe O.?. consists in determining the initial speed of a load that is suspended from a spring and performs free vertical oscillations with an amplitude of 0.1 m. It is known that the mass of the load is 9 kg, and the spring stiffness coefficient is 90 N/m.

To solve the problem, it is necessary to use the law of conservation of energy, according to which the total mechanical energy of the system remains constant. At the initial moment of time, the load is in a position of static equilibrium, so its potential energy is zero, and its kinetic energy is maximum.

At the maximum deviation of the load from the equilibrium position, its potential energy is maximum, and its kinetic energy is zero. From the law of conservation of energy it follows that the total mechanical energy at these two points is equal to each other.

Thus, we can write the energy conservation equation:

mgh = (1/2)kx^2,

where m is the mass of the load, g is the acceleration of gravity, h is the maximum deviation of the load from the equilibrium position (oscillation amplitude), k is the spring stiffness coefficient, x is the maximum deviation of the spring from the equilibrium position (also equal to the oscillation amplitude).

Expressing the initial speed of the load in terms of known quantities, we obtain:

v = sqrt(2gh),

where sqrt is the square root.

Substituting the values ​​from the problem conditions, we get:

v = sqrt(2 * 9.81 m/s^2 * 0.1 m) ≈ 0.316 m/s.

Answer: the initial speed of the load is 0.316 m/s.

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