Question

Два маятника, довжини яких відрізняються на 22 см, здійснюють в тому самому місці за деякий час один 30 коливань, другий – 36 коливань. Знайти довжини маятників.

Answer 1

Ответ:

Объяснение:Дано:

l₂ = l₁ + 0,22 м

N₁ = 36

N₂ = 30

t₁ = t₂ = t

Найти:

l₁ - ?

l₂ - ?

Решение:

T = 2π√ (l/g); T = t/N

t/N₁ = 2π√ (l₁/g)

t/N₂ = 2π√ ((l₁ + 0,22) / g)

2πN₁√ (l₁/g) = 2πN₂√ ((l₁ + 0,22) / g)

N₁√l₁ = N₂√ (l₁ + 0,22)

N₁² l₁ = N₂² (l₁ + 0,22)

l₁ (N₁² - N₂²) = 0,22 N₂²

l₁ = 0,22 N₂² / (N₁ - N₂) (N₁ + N₂)

l₁ = 0,22 м * 30² / (36 - 30) (36 + 30) = 0,5 м

l₁ = 0,5 м

l₂ = 0,5 м + 0,22 м = 0,72 м

Answer 2

Finding the Lengths of the Pendulums

To find the lengths of the pendulums, we can use the formula for the period of a simple pendulum:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Let's assume that the length of the first pendulum is L1 and the length of the second pendulum is L2. We are given the following information:

- The difference in length between the two pendulums is 22 cm. - The first pendulum completes 30 oscillations in a certain time. - The second pendulum completes 36 oscillations in the same time.

Using the formula for the period, we can set up the following equations:

T1 = 2π√(L1/g) T2 = 2π√(L2/g)

We can rearrange these equations to solve for L1 and L2:

L1 = (T1/2π)² * g L2 = (T2/2π)² * g

Since the time is the same for both pendulums, we can set T1 equal to T2:

L1 = L2

Now we can substitute the given values into the equations and solve for L1 and L2.

Let's calculate the lengths of the pendulums using the given information.

Calculation:

Given: - Difference in length between the two pendulums = 22 cm - Number of oscillations for the first pendulum = 30 - Number of oscillations for the second pendulum = 36

Using the formula for the period of a pendulum, we can calculate the lengths of the pendulums.

Let's assume the length of the first pendulum is L1 and the length of the second pendulum is L2.

From the given information, we have:

T1 = 30 oscillations T2 = 36 oscillations

Using the formula for the period of a pendulum, we have:

T1 = 2π√(L1/g) T2 = 2π√(L2/g)

Since the time is the same for both pendulums, we can set T1 equal to T2:

T1 = T2

Substituting the given values, we have:

2π√(L1/g) = 2π√(L2/g)

Simplifying the equation, we have:

√(L1/g) = √(L2/g)

Squaring both sides of the equation, we have:

L1/g = L2/g

Since the acceleration due to gravity (g) is the same for both pendulums, we can cancel it out:

L1 = L2

Therefore, the lengths of the two pendulums are equal.

Now, let's calculate the length of the pendulums using the given information.

Substituting the values into the equation, we have:

L1 = L2 = 22 cm

Therefore, the lengths of the pendulums are both 22 cm.

Answer:

The lengths of both pendulums are 22 cm.