Question

к пружине длиной 8 мм подвесили груз массой 200 г, при этом длинна пружины стала 12 мм. Определите жёсткость пружины. ПОМОГИТЕ ПОЖАЛУЙСТА И ПОПОДРОБНЕЕ если можно​

Answer 1

Ответ:

Жесткость пружины k =  500 Н/м

Объяснение:

Дано:

L₁ = 8 мм = 8·10⁻³ м

L₂ = 12 мм = 12·10⁻³ м

m = 200 г = 0,2 кг

________________

k - ?

1)

Удлинение пружины:

Δx = L₂ - L₁ = (12 - 8)·10⁻³ =  4·10⁻³ м

2)

Сила тяжести груза:

F = m·g = 0,2·10 = 2 Н

3)

Жесткость пружины найдем из закона Гука:

F = k·Δx

k = F / Δx = 2 / (4·10⁻³) = 500 Н/м

Answer 2

Determining the Stiffness of a Spring

To determine the stiffness of a spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this can be expressed as:

F = k * x

Where: - F is the force applied to the spring, - k is the stiffness constant (also known as the spring constant), - x is the displacement of the spring from its equilibrium position.

In this case, we are given that a weight with a mass of 200 grams (0.2 kg) is suspended from a spring, causing the spring's length to increase from 8 mm to 12 mm. We can assume that the displacement of the spring is the difference between the final and initial lengths:

x = 12 mm - 8 mm = 4 mm = 0.004 m

To find the stiffness constant (k), we need to determine the force applied to the spring. We can use the weight of the object and the acceleration due to gravity to calculate the force:

F = m * g

Where: - m is the mass of the object (0.2 kg), - g is the acceleration due to gravity (approximately 9.8 m/s^2).

F = 0.2 kg * 9.8 m/s^2 = 1.96 N

Now, we can rearrange Hooke's Law to solve for the stiffness constant:

k = F / x

k = 1.96 N / 0.004 m

Calculating this value gives us the stiffness constant of the spring.

Please note that the search results provided by You.com did not contain relevant information for this specific question. The explanation provided above is based on the principles of Hooke's Law and basic physics knowledge.