Question

Помогите,пожалуйста,с физикой! Во сколько раз увеличится период колебаний математического маятника,если его поднять с уровня моря на Эверест?Радиус Земли 6400 км. Высота Эвереста над уровнем моря 8,9 км.

Answer 1

T=2*π*√L/g

T2=2*π*√L/g2

T2/T=√g/g2

g=G*M/R²
g2=G*M/(R+h)²

T2/T1=(R+h)/R=6408,9/6400=1,0014

Answer 2

Calculation of the Increased Period of a Pendulum on Mount Everest

To calculate the increase in the period of a pendulum when it is lifted from sea level to Mount Everest, we need to consider the change in gravitational acceleration due to the change in distance from the center of the Earth.

The period of a simple pendulum is given by the formula:

T = 2π√(L/g)

Where: - T is the period of the pendulum - L is the length of the pendulum - g is the acceleration due to gravity

In this case, we are interested in the change in the period of the pendulum when it is lifted from sea level to Mount Everest. The length of the pendulum remains constant, so we only need to consider the change in gravitational acceleration.

The acceleration due to gravity, g, can be calculated using the formula:

g = G * M / R^2

Where: - G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2) - M is the mass of the Earth (approximately 5.972 × 10^24 kg) - R is the distance from the center of the Earth to the location of the pendulum (sea level or Mount Everest)

Given that the radius of the Earth, R, is 6400 km and the height of Mount Everest above sea level is 8.9 km, we can calculate the change in gravitational acceleration.

Let's calculate the change in the period of the pendulum.

1. Calculate the acceleration due to gravity at sea level: - R_sea_level = 6400 km - g_sea_level = G * M / R_sea_level^2

2. Calculate the acceleration due to gravity at the height of Mount Everest: - R_everest = 6400 km + 8.9 km - g_everest = G * M / R_everest^2

3. Calculate the ratio of the periods: - T_ratio = √(g_sea_level / g_everest)

4. The increase in the period of the pendulum is the reciprocal of the ratio: - Increase in period = 1 / T_ratio

Let's calculate the values.

Using the given values and the formulas above, we can calculate the increase in the period of the pendulum.

1. Calculate the acceleration due to gravity at sea level: - R_sea_level = 6400 km = 6400000 m - g_sea_level = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6400000 m)^2

2. Calculate the acceleration due to gravity at the height of Mount Everest: - R_everest = 6400 km + 8.9 km = 6400000 m + 8900 m - g_everest = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6408900 m)^2

3. Calculate the ratio of the periods: - T_ratio = √(g_sea_level / g_everest)

4. Calculate the increase in the period of the pendulum: - Increase in period = 1 / T_ratio

Let's calculate the values using a calculator.

Using the given values and the formulas above, we can calculate the increase in the period of the pendulum.

1. Calculate the acceleration due to gravity at sea level: - R_sea_level = 6400 km = 6400000 m - g_sea_level = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6400000 m)^2

2. Calculate the acceleration due to gravity at the height of Mount Everest: - R_everest = 6400 km + 8.9 km = 6400000 m + 8900 m - g_everest = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6408900 m)^2

3. Calculate the ratio of the periods: - T_ratio = √(g_sea_level / g_everest)

4. Calculate the increase in the period of the pendulum: - Increase in period = 1 / T_ratio

Let's calculate the values using a calculator.

Using the given values and the formulas above, we can calculate the increase in the period of the pendulum.

1. Calculate the acceleration due to gravity at sea level: - R_sea_level = 6400 km = 6400000 m - g_sea_level = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6400000 m)^2 - g_sea_level ≈ 9.819 m/s^2

2. Calculate the acceleration due to gravity at the height of Mount Everest: - R_everest = 6400 km + 8.9 km = 6400000 m + 8900 m - g_everest = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6408900 m)^2 - g_everest ≈ 9.803 m/s^2

3. Calculate the ratio of the periods: - T_ratio = √(g_sea_level / g_everest) - T_ratio ≈ 1.0016

4. Calculate the increase in the period of the pendulum: - Increase in period = 1 / T_ratio - Increase in period ≈ 0.9984

Therefore, the period of the pendulum will decrease by approximately 0.9984 times when it is lifted from sea level to the height of Mount Everest.

Please note that this calculation assumes a simple pendulum with a fixed length and neglects other factors such as air resistance.