Question

Помогите пожалуйста.... Определите жёсткость пружины, на которой висит груз массой 500г, если он совершает колебания с амплитудой 0,1м и скоростью 5м/с?​

Answer 1

Ответ:

........................................

Answer 2

Ответ:

Объяснение:

Дано:

m = 500 г = 0,5 кг

A = 0,1 м

V = 5 м/с

_______________

k - ?

1)

Циклическая частота:

ω = √ (k/m)             (1)

2)

Скорость:

V = ω·A

ω = V / A                 (2)

3)

Приравняем:

√ (k/m) = V / A

k / m = V² / A²

Жесткость:

k = m·V² / A²

k = 0,5·5² / (0,1)² = 1250 Н/м

Answer 3

Calculating the Spring Constant

To determine the spring constant, we can use the formula for the potential energy of a spring:

Potential energy (U) = 0.5 * k * x^2

Where: - U = potential energy - k = spring constant - x = displacement from the equilibrium position

We can rearrange the formula to solve for the spring constant (k):

k = (2 * U) / x^2

Given that the mass (m) = 500g = 0.5kg, amplitude (A) = 0.1m, and velocity (v) = 5m/s, we can calculate the potential energy (U) and then use it to find the spring constant (k).

Calculating Potential Energy

The potential energy of the oscillating mass can be calculated using the formula:

Potential energy (U) = 0.5 * m * v^2

Where: - m = mass - v = velocity

Substituting the given values, we get:

U = 0.5 * 0.5kg * (5m/s)^2

U = 0.5 * 0.5kg * 25m^2/s^2

U = 6.25J

Finding the Spring Constant

Now, we can use the potential energy (U) to find the spring constant (k) using the formula:

k = (2 * U) / A^2

Substituting the values, we get:

k = (2 * 6.25J) / (0.1m)^2

k = 12.5J / 0.01m^2

k = 1250 N/m

So, the spring constant of the spring on which the mass is hanging is 1250 N/m. [[1]]