Question

во сколько раз изменится полная механическая энергия колеблющегося маятника при уменьшении его длины в 3 раза и увеличении амплитуды колебаний в 2 раза?........РЕШИТЕ ПОЖАЛУЙСТА ПЯМО ЩАС!!!

Answer 1

вот наверно вот так. Думаю правильно. 

Answer 2

Calculation of Change in Total Mechanical Energy of a Pendulum

To calculate the change in the total mechanical energy of a pendulum when its length is reduced by 3 times and the amplitude of oscillation is increased by 2 times, we need to consider the factors that affect the mechanical energy of a pendulum.

The total mechanical energy of a pendulum is the sum of its potential energy and kinetic energy. The potential energy is given by the equation:

Potential Energy (PE) = mgh

where: - m is the mass of the pendulum bob, - g is the acceleration due to gravity, and - h is the height of the pendulum bob above its lowest point.

The kinetic energy is given by the equation:

Kinetic Energy (KE) = (1/2)mv^2

where: - m is the mass of the pendulum bob, and - v is the velocity of the pendulum bob.

The total mechanical energy (E) is the sum of the potential energy and kinetic energy:

Total Mechanical Energy (E) = PE + KE

To calculate the change in the total mechanical energy, we need to compare the initial and final states of the pendulum.

Let's assume the initial length of the pendulum is L, and the initial amplitude of oscillation is A. After reducing the length by 3 times, the new length becomes L/3. After increasing the amplitude by 2 times, the new amplitude becomes 2A.

Now, let's calculate the change in the total mechanical energy.

Calculation Steps:

1. Calculate the initial potential energy (PE_initial) and initial kinetic energy (KE_initial) of the pendulum using the initial length (L) and amplitude (A). 2. Calculate the final potential energy (PE_final) and final kinetic energy (KE_final) of the pendulum using the new length (L/3) and amplitude (2A). 3. Calculate the change in potential energy (ΔPE) by subtracting PE_initial from PE_final. 4. Calculate the change in kinetic energy (ΔKE) by subtracting KE_initial from KE_final. 5. Calculate the change in total mechanical energy (ΔE) by adding ΔPE and ΔKE.

Let's perform the calculations step by step.

Step 1: Calculate the initial potential energy (PE_initial) and initial kinetic energy (KE_initial):

The initial potential energy (PE_initial) is given by the equation PE_initial = mgh, where h is the height of the pendulum bob above its lowest point. Since the pendulum bob is at its highest point at the amplitude, h = A.

The initial kinetic energy (KE_initial) is given by the equation KE_initial = (1/2)mv^2, where v is the velocity of the pendulum bob. At the highest point of the pendulum's swing, the velocity is zero.

Therefore, KE_initial = 0.

Step 2: Calculate the final potential energy (PE_final) and final kinetic energy (KE_final):

The final potential energy (PE_final) is given by the equation PE_final = mgh, where h is the height of the pendulum bob above its lowest point. Since the pendulum bob is at its highest point at the amplitude, h = 2A.

The final kinetic energy (KE_final) is given by the equation KE_final = (1/2)mv^2, where v is the velocity of the pendulum bob. At the highest point of the pendulum's swing, the velocity is zero.

Therefore, KE_final = 0.

Step 3: Calculate the change in potential energy (ΔPE):

ΔPE = PE_final - PE_initial = mgh_final - mgh_initial = mg(2A) - mg(A) = mgA.

Step 4: Calculate the change in kinetic energy (ΔKE):

ΔKE = KE_final - KE_initial = 0 - 0 = 0.

Step 5: Calculate the change in total mechanical energy (ΔE):

ΔE = ΔPE + ΔKE = mgA + 0 = mgA.

Therefore, the change in the total mechanical energy of the pendulum when its length is reduced by 3 times and the amplitude of oscillation is increased by 2 times is mgA.

Please note that the above calculations assume ideal conditions and neglect any losses due to friction or air resistance.