Question

На сколько секунд увеличится период колебаний математического маятника длиной 9,8 м при изменении температуры окружающей среды от 0°C до 300°С , если коэффициент линейного расширения материала нити равен 0.0007 К-1 ?

Answer 1

Ответ:

Объяснение:

Период был:

T₁ = 2π·√ (L₁/g) = 2π·√ (9,8 / 9,8) = 2π с

Длина маятника после нагревания:

L₂ = L₁·(1 + α·T) = 9,8·( 1 + 0,0007·300) = 9,8·1,21 м

Период стал:

T₂ = 2π·√ (L₂/g) = 2π·√ (9,8·1,21 / 9,8) = 2π·√(1,21) = 2π·1,1  с

Период увеличился на:

ΔT = T₂ - T₁ = 2π· (1,1 - 1) = 0,2·π = 0,2·3,14 = 0,63 с

Answer 2

Calculating the Change in Period of a Pendulum Due to Temperature Change

To calculate the change in the period of a pendulum due to a change in temperature, we can use the formula for the change in the period of a pendulum with respect to temperature. The formula is given by:

ΔT = α * T * ΔL

Where: - ΔT is the change in the period of the pendulum - α is the coefficient of linear expansion of the material - T is the original temperature - ΔL is the change in length of the pendulum due to the change in temperature

Given: - Length of the pendulum, L = 9.8 m - Coefficient of linear expansion, α = 0.0007 K^-1 - Change in temperature, ΔT = 300°C - 0°C = 300 K

We can calculate the change in the period of the pendulum using the above formula.

Calculating the Change in Length of the Pendulum Due to Temperature Change

The change in length of the pendulum due to the change in temperature can be calculated using the formula:

ΔL = L * α * ΔT

Where: - ΔL is the change in length of the pendulum - L is the original length of the pendulum - α is the coefficient of linear expansion of the material - ΔT is the change in temperature

Given: - Length of the pendulum, L = 9.8 m - Coefficient of linear expansion, α = 0.0007 K^-1 - Change in temperature, ΔT = 300 K

We can calculate the change in length of the pendulum using the above formula.

Calculation

Using the given values and the formulas, we can calculate the change in length of the pendulum and then use it to calculate the change in the period of the pendulum.

Calculating ΔL: ΔL = L * α * ΔT = 9.8 m * 0.0007 K^-1 * 300 K = 2.058 m

Calculating ΔT: ΔT = α * T * ΔL = 0.0007 K^-1 * 300 K * 2.058 m ≈ 0.43 s

Conclusion

The period of the mathematical pendulum with a length of 9.8 m will increase by approximately 0.43 seconds due to the change in temperature from 0°C to 300°C, given a coefficient of linear expansion of 0.0007 K^-1 for the material of the pendulum.