Question

На какое расстояние надо отвести от положения равновесия груз массой 640г, закрепленный на пружине жесткостью 0,4 кН/м, чтобы он проходил положение равновесия со скоростью 1м/с?

Answer 1

 

Закон сохранения энергии

Е=mv^2/2=kx^2/2

х=v*sqrt m/k = 1м/с*sqrt 0.64кг/400 Н/м = 0,04м

Answer 2

Calculating the Displacement from Equilibrium Position

To calculate the displacement from the equilibrium position for a mass of 640g attached to a spring with a stiffness of 0.4 kN/m, we can use the formula for the potential energy of a spring:

Potential Energy of a Spring (U) = 0.5 * k * x^2

Where: - k = stiffness of the spring (0.4 kN/m) - x = displacement from the equilibrium position

We can rearrange the formula to solve for x:

x = sqrt(2 * U / k)

Given that the mass passes through the equilibrium position with a velocity of 1 m/s, we can use the kinetic energy formula to find the displacement from the equilibrium position:

Kinetic Energy (K) = 0.5 * m * v^2

Where: - m = mass (640g = 0.64kg) - v = velocity (1 m/s)

We can equate the potential energy at the equilibrium position to the kinetic energy at the maximum displacement to solve for x.

Calculation

Using the given values: - Mass (m) = 0.64 kg - Stiffness of the spring (k) = 0.4 kN/m - Velocity (v) = 1 m/s

We can calculate the displacement (x) from the equilibrium position using the formula:

x = sqrt(2 * K / k)

Substituting the values: x = sqrt(2 * (0.5 * 0.64 * 1^2) / 0.4)

x = sqrt(0.8 / 0.4) = sqrt(2) ≈ 1.414 m

So, the displacement from the equilibrium position for the given conditions is approximately 1.414 meters.