Question

Срочно!(с полным решением) При гармонических колебаниях тела на пружине максимальное значение его кинетической энергии равно 20 Дж, максимальное значение потенциальной энергии пружины 20 Дж.Как изменится во времени полная механическая энергия тела и пружины? Заранее большое спасибо!

Answer 1

Ek max =Ep max =E
В момент, когда энергия потенциальная максимальна, кинетическая энергия равна 0. В момент, когда кинетическая энергия максимальна, потенциальная энергия колеблющегося тела равна 0.
Полная энергия E=Ek+Ep =сonst. Таким образом E полная не меняется и равна 20 Дж.

Answer 2

По закону сохранения энергии : Ек=Е деформаци(или энергия деформированного тела)

Ответ: 30 Дж

Answer 3

Solution for Changes in Total Mechanical Energy

When a body undergoes harmonic oscillations on a spring, the total mechanical energy of the body and the spring changes over time. Given that the maximum value of the kinetic energy of the body is 20 J and the maximum value of the potential energy of the spring is also 20 J, we can analyze the changes in the total mechanical energy of the system.

The total mechanical energy of the system, which includes the kinetic energy of the body and the potential energy of the spring, is given by the sum of these two energies.

Step 1: Calculating Total Mechanical Energy The total mechanical energy (E) of the system is the sum of the kinetic energy (K) and the potential energy (U) at any given time. Mathematically, it can be expressed as: E = K + U

Step 2: Analyzing Changes in Total Mechanical Energy When the body undergoes harmonic oscillations, the total mechanical energy of the system remains constant. This is due to the conservation of mechanical energy in the absence of non-conservative forces such as friction.

However, it's important to note that the energy oscillates between kinetic and potential forms during the oscillations, but the total mechanical energy remains constant.

Therefore, the total mechanical energy of the body and the spring will not change over time. It will remain constant at the sum of the maximum kinetic and potential energies, which is 40 J.

In summary, the total mechanical energy of the body and the spring will not change over time during harmonic oscillations.

Conclusion: The total mechanical energy of the body and the spring will remain constant at 40 J throughout the harmonic oscillations.