Question

Шарик, подвешенный на нити отклонили влево и отпускают. через какую долю периода кинетическая энергия маятника будет максимальной

Answer 1

Через 1/4 периода (за период 2 раза максимум энергии)

Answer 2

Calculating the Maximum Kinetic Energy of a Pendulum

When a pendulum is released after being deflected to one side, its kinetic energy will be maximum at a certain point during its motion. Let's calculate the fraction of the period at which the kinetic energy of the pendulum will be at its maximum.

The maximum kinetic energy of a pendulum occurs when it is at the lowest point of its swing, which is also the point of maximum speed. At this point, all the potential energy has been converted to kinetic energy.

The period of a pendulum is the time it takes for the pendulum to complete one full oscillation, i.e., to swing from one extreme point to the other and back again.

To find the fraction of the period at which the kinetic energy of the pendulum will be maximum, we can use the relationship between kinetic energy and potential energy in a pendulum.

The kinetic energy (KE) and potential energy (PE) of a pendulum are related by the equation: KE = (1/2) * m * v^2 where m is the mass of the pendulum and v is its velocity.

The potential energy (PE) of a pendulum is given by: PE = m * g * h where m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height of the pendulum above its lowest point.

At the lowest point of the swing, the height h is zero, so the potential energy is zero, and all the energy is in the form of kinetic energy.

Using the relationship between kinetic and potential energy, we can calculate the fraction of the period at which the kinetic energy of the pendulum will be maximum.

According to the search results, the relevant information for this specific calculation is not available. Therefore, I recommend consulting a physics textbook or academic resource for a detailed explanation of the calculation.