Question

деревянный брусок массой 2 кг тянут равномерно по деревянной доске, расположенной горизонтально, с помощью пружины с жёсткостью 100 Н/м. Коэффициент трения равен 0,3. найти удлинение пружины.

Answer 1

Problem Analysis

We are given a wooden block with a mass of 2 kg being pulled uniformly across a horizontal wooden board using a spring with a stiffness of 100 N/m. The coefficient of friction between the block and the board is 0.3. We need to find the elongation of the spring.

Solution

To find the elongation of the spring, we can use the concept of equilibrium. When the block is pulled, the force exerted by the spring is balanced by the force of friction and the weight of the block.

Let's break down the problem step by step:

1. Calculate the force of gravity acting on the block. 2. Calculate the force of friction between the block and the board. 3. Calculate the force exerted by the spring. 4. Set up an equation using the forces in equilibrium. 5. Solve the equation to find the elongation of the spring.

Step 1: Calculate the force of gravity

The force of gravity acting on the block can be calculated using the formula:

Force of gravity = mass x acceleration due to gravity

Given that the mass of the block is 2 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force of gravity.

Force of gravity = 2 kg x 9.8 m/s^2

Step 2: Calculate the force of friction

The force of friction can be calculated using the formula:

Force of friction = coefficient of friction x normal force

The normal force is equal to the force of gravity acting on the block.

Force of friction = 0.3 x (2 kg x 9.8 m/s^2)

Step 3: Calculate the force exerted by the spring

The force exerted by the spring can be calculated using Hooke's Law:

Force exerted by the spring = spring constant x elongation of the spring

The spring constant is given as 100 N/m. We need to find the elongation of the spring.

Step 4: Set up an equation using the forces in equilibrium

In equilibrium, the force exerted by the spring is balanced by the force of friction and the force of gravity. Therefore, we can set up the following equation:

Force exerted by the spring = Force of friction + Force of gravity

Step 5: Solve the equation to find the elongation of the spring

Substituting the values we calculated earlier, we can solve the equation to find the elongation of the spring.

100 N/m x elongation of the spring = (0.3 x (2 kg x 9.8 m/s^2)) + (2 kg x 9.8 m/s^2)

Simplifying the equation, we can solve for the elongation of the spring.

Now let's calculate the elongation of the spring using the given values.

Elongation of the spring = (0.3 x (2 kg x 9.8 m/s^2) + (2 kg x 9.8 m/s^2)) / 100 N/m

Calculating the above expression will give us the elongation of the spring.

Answer

The elongation of the spring is approximately 0.58 meters.