Question

СРОЧНО ПОМОГИТЕ!!!!! ДАМ 100 БАЛЛОВ!!!!!!!!Пружинный маятник, совершает колебания в горизонтальной плоскости(пружина прикреплена к стене). Жесткость пружины 1700 Н/м. Кинетическая энергия шарика, при прохождении через положение равновесия равна 19 Дж. Найдите амплитуду колебаний. Ответ, полученный в метрах округлить до тысячных и выразить в миллиметрах. В процессе вычислений, округлений не производить..

Answer 1

Ответ:

50 КДЖ

Объяснение:

СРОЧНО ПОМОГИТЕ!!!!! ДАМ 100 БАЛЛОВ!!!!!!!!Пружинный маятник, совершает колебания в горизонтальной плоскости(пружина прикреплена к стене). Жесткость пружины 1700 Н/м. Кинетическая энергия шарика, при прохождении через положение равновесия равна 19 Дж. Найдите амплитуду колебаний. Ответ, полученный в метрах округлить до тысячных и выразить в миллиметрах. В процессе вычислений, округлений не производить..

Answer 2

Calculation of the Amplitude of Oscillations

To find the amplitude of oscillations of the spring pendulum, we can use the formula for the total mechanical energy of the system. The total mechanical energy is the sum of the potential energy and the kinetic energy.

The potential energy of the spring is given by the formula:

Potential Energy (PE) = (1/2) * k * x^2

where k is the spring constant (also known as the stiffness of the spring) and x is the displacement from the equilibrium position.

The kinetic energy of the ball is given by the formula:

Kinetic Energy (KE) = (1/2) * m * v^2

where m is the mass of the ball and v is its velocity.

Since the ball passes through the equilibrium position, its velocity is maximum at that point. Therefore, the kinetic energy at the equilibrium position is equal to the total mechanical energy of the system.

Given that the kinetic energy at the equilibrium position is 19 J, we can equate it to the sum of the potential energy and the kinetic energy:

19 J = (1/2) * k * x^2 + (1/2) * m * v^2

We are given the stiffness of the spring (k = 1700 N/m) and the mass of the ball is not provided. However, we can solve for the amplitude of oscillations without knowing the mass of the ball.

Since the ball passes through the equilibrium position, the potential energy at the equilibrium position is zero. Therefore, we can simplify the equation to:

19 J = (1/2) * m * v^2

Now, let's solve for the amplitude of oscillations.

Solving for the Amplitude

To find the amplitude of oscillations, we need to determine the maximum velocity of the ball at the equilibrium position. We can use the formula for the maximum velocity of a mass-spring system:

Maximum Velocity (v_max) = A * ω

where A is the amplitude of oscillations and ω is the angular frequency of the system.

The angular frequency can be calculated using the formula:

Angular Frequency (ω) = √(k / m)

where k is the spring constant and m is the mass of the ball.

Since we don't know the mass of the ball, we can express the amplitude of oscillations in terms of the maximum velocity and the angular frequency:

A = v_max / ω

To find the maximum velocity, we can use the equation for kinetic energy:

19 J = (1/2) * m * v_max^2

Solving for v_max:

v_max = √(38 J / m)

Substituting the expressions for v_max and ω into the equation for the amplitude:

A = √(38 J / m) / √(k / m)

Simplifying the expression:

A = √(38 J * m / k)

Given that k = 1700 N/m, we can substitute this value into the equation:

A = √(38 J * m / 1700 N/m)

To express the amplitude in meters and round it to the nearest thousandth, we need to convert it to millimeters. There are 1000 millimeters in a meter, so we multiply the amplitude by 1000:

A (in millimeters) = √(38 J * m / 1700 N/m) * 1000

Unfortunately, we don't have the value of the mass of the ball, so we cannot calculate the amplitude without that information. Please provide the mass of the ball to proceed with the calculation.