Question

Растянутая на 2 см пружина, сокращаясь, увлекает за собой тело по горизонтальной плоскости без трения. В момент, когда деформация пружины равна нулю, скорость тело равна 6 м/с. Чему равна масса тела, если жесткость пружины равна 45kH/м

Answer 1

Теперь просто поставь эти значения в формулу и все: m=8 V0=(2м/с)^2 k=8кН/м = 8000 Н/м ответ: 0.02м=2 см.

Answer 2

Problem Analysis

We are given a scenario where a spring, initially stretched by 2 cm, contracts and pulls a body along a horizontal plane without friction. We are also given that when the deformation of the spring is zero, the velocity of the body is 6 m/s. We need to find the mass of the body, given that the spring's stiffness is 45 kH/m.

Solution

To solve this problem, we can use the principle of conservation of mechanical energy. The initial potential energy stored in the spring is equal to the final kinetic energy of the body.

Let's denote the initial deformation of the spring as x (2 cm or 0.02 m), the final deformation as 0 (zero), the initial velocity of the body as 0 (since it starts from rest), and the final velocity as 6 m/s.

The potential energy stored in the spring is given by the formula:

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

where k is the stiffness of the spring.

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

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

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

Since the potential energy is converted into kinetic energy, we can equate the two expressions:

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

Now we can solve for the mass m:

m = (k * x^2) / v^2

Substituting the given values:

m = (45 kH/m * (0.02 m)^2) / (6 m/s)^2

Calculation

Let's calculate the mass of the body using the given values:

m = (45 * 0.02^2) / 6^2

m ≈ 0.0003 kg

Therefore, the mass of the body is approximately 0.0003 kg.

Answer

The mass of the body is approximately 0.0003 kg.