Question

Нитяной маятник за 1 минуту совершил 15 полных колебаний. Сколько колебаний за 30 секунд совершит этот маятник, если его длину увеличить в два раза? Подробно.

Answer 1

Так как с увеличением длины маятника период увеличивается, а значит количество колебаний уменьшается в 2 раза, потому, что уменьшается во столько раз во сколько увеличилась его длина, причём время для колебаний уменьшили в 2 раза, тогда 15:4=3целых, 3/4 колебаний совершит маятник.

Answer 2

Calculation of the Number of Oscillations

To determine the number of oscillations the pendulum will make in 30 seconds, we need to consider the relationship between the length of the pendulum and the time it takes to complete one oscillation.

Let's analyze the given information: - The pendulum completed 15 full oscillations in 1 minute (60 seconds). - The length of the pendulum is being doubled.

To find the number of oscillations in 30 seconds, we can use the formula:

Number of Oscillations = (Time / Period)

Where: - Time is the duration in seconds (30 seconds in this case). - Period is the time taken for one complete oscillation.

To find the period, we can use the formula:

Period = 1 / Frequency

Where: - Frequency is the number of oscillations per second.

To find the frequency, we can use the formula:

Frequency = 1 / Time per Oscillation

Where: - Time per Oscillation is the time taken for one oscillation.

Now, let's calculate the number of oscillations in 30 seconds.

Calculation Steps:

1. Calculate the period of the pendulum after doubling its length. 2. Calculate the frequency of the pendulum after doubling its length. 3. Calculate the time per oscillation of the pendulum after doubling its length. 4. Calculate the number of oscillations in 30 seconds using the time per oscillation.

Step 1: Calculate the Period

The period of the pendulum is the time taken for one complete oscillation. To calculate the period, we can use the formula:

Period = 1 / Frequency

Since the frequency is the number of oscillations per second, we can calculate the period by dividing 1 by the frequency.

Let's calculate the period of the pendulum after doubling its length.

Period = 1 / Frequency

Period = 1 / (15 oscillations / 60 seconds)

Period = 1 / (0.25 oscillations/second)

Period = 4 seconds

Step 2: Calculate the Frequency

The frequency of the pendulum is the number of oscillations per second. To calculate the frequency, we can use the formula:

Frequency = 1 / Time per Oscillation

Let's calculate the frequency of the pendulum after doubling its length.

Frequency = 1 / Time per Oscillation

Frequency = 1 / (4 seconds/oscillation)

Frequency = 0.25 oscillations/second

Step 3: Calculate the Time per Oscillation

The time per oscillation is the time taken for one oscillation. To calculate the time per oscillation, we can use the formula:

Time per Oscillation = Period

Let's calculate the time per oscillation of the pendulum after doubling its length.

Time per Oscillation = Period

Time per Oscillation = 4 seconds

Step 4: Calculate the Number of Oscillations in 30 Seconds

Now that we have the time per oscillation, we can calculate the number of oscillations in 30 seconds using the formula:

Number of Oscillations = Time / Period

Number of Oscillations = 30 seconds / 4 seconds

Number of Oscillations = 7.5 oscillations

Therefore, if the length of the pendulum is doubled, it will complete approximately 7.5 oscillations in 30 seconds.

Please note that the calculated value is an approximation since the actual number of oscillations may not be a whole number.