Question

Вагоне поезда подвешен маятник длиной 1 м. При движении поезда маятник раскачивается от толчков на стыках рельсов. При какой скорости поезда маятник раскачивается особенно сильно, если длина рельсов 25 м

Answer 1

Особенное сильное раскачивание (резонанс) будет, если поезд станет проходить стык рельсов в момент прохождения маятника через положение равновесия, то есть дважды за период.
$T = 2*pi \sqrt{ \frac{l}{g} } = 2 c$
$\frac{T}{2} = 1c$
v = 25 м/с = 90 км/ч

Answer 2

Calculation of the Speed at which the Pendulum Swings Strongly

To determine the speed at which the pendulum swings strongly, we need to consider the length of the pendulum and the length of the rails. In this case, the length of the pendulum is given as 1 meter, and the length of the rails is 25 meters.

The speed at which the pendulum swings strongly can be calculated using the formula for the period of a simple pendulum:

T = 2π√(L/g)

Where: - T is the period of the pendulum (time taken for one complete swing) - L is the length of the pendulum - g is the acceleration due to gravity (approximately 9.8 m/s^2)

In this case, the length of the pendulum is 1 meter. Plugging in the values, we can calculate the period of the pendulum:

T = 2π√(1/9.8) ≈ 2π√(0.102) ≈ 2π * 0.319 ≈ 2.006 seconds

The period of the pendulum is approximately 2.006 seconds.

To calculate the speed at which the pendulum swings strongly, we can use the formula:

Speed = Distance / Time

In this case, the distance traveled by the pendulum is equal to the length of the rails, which is 25 meters. The time taken for one complete swing (the period) is approximately 2.006 seconds. Plugging in the values, we can calculate the speed:

Speed = 25 meters / 2.006 seconds ≈ 12.47 meters per second

Therefore, the pendulum swings strongly when the speed of the train is approximately 12.47 meters per second.

Please note that the above calculation assumes ideal conditions and does not take into account factors such as air resistance or friction.