Question

На опорах лежит длинная труба массой m=10 кг. Расстояние от левого края трубы до левой опоры = 10 см,расстояние между опорами= 40 см, длина трубы = 80 см. Какую силу F, направленную вертикально вниз, надо приложить к левому концу трубки, чтобы труба не давила на правую опору?

Answer 1

L - длина трубы
d - расстояние от левого края до левой опоры
по правилу моментов выбрать за ось вращения левую опору и приняв реакцию правой опоры равной нулю получаем
F*d = mg*(L/2-d)
F=mg*(L/2-d)/d=10*10*(0,8/2-0,1)/0,1 Н= 300 Н - это ответ

Answer 2

Problem Analysis

We are given a long pipe with a mass of 10 kg, supported by two pillars. The distance from the left edge of the pipe to the left pillar is 10 cm, the distance between the pillars is 40 cm, and the length of the pipe is 80 cm. We need to find the force F that needs to be applied vertically downward at the left end of the pipe to prevent it from pressing against the right pillar.

Solution

To solve this problem, we can use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.

Let's consider the left pillar as the point of rotation. The weight of the pipe acts vertically downward and can be considered as a force applied at the center of mass of the pipe. The force F applied at the left end of the pipe also acts vertically downward. The distance between the left end of the pipe and the left pillar is 10 cm, and the distance between the left end of the pipe and the center of mass of the pipe is 40 cm.

Using the principle of moments, we can write the equation:

Clockwise moments = Anticlockwise moments

The clockwise moments are given by the weight of the pipe, which is the mass of the pipe multiplied by the acceleration due to gravity (g), multiplied by the distance between the center of mass of the pipe and the left pillar.

The anticlockwise moments are given by the force F applied at the left end of the pipe, multiplied by the distance between the left end of the pipe and the left pillar.

Mathematically, we can write:

(m * g * l1) = (F * l2)

where: - m is the mass of the pipe (10 kg) - g is the acceleration due to gravity (9.8 m/s^2) - l1 is the distance between the center of mass of the pipe and the left pillar (40 cm = 0.4 m) - F is the force applied at the left end of the pipe (unknown) - l2 is the distance between the left end of the pipe and the left pillar (10 cm = 0.1 m)

Now, let's solve the equation to find the value of F.

Calculation

Substituting the given values into the equation, we have:

(10 kg * 9.8 m/s^2 * 0.4 m) = (F * 0.1 m)

Simplifying the equation, we get:

F = (10 kg * 9.8 m/s^2 * 0.4 m) / 0.1 m

Calculating the value, we find:

F = 392 N

Therefore, a force of 392 N, directed vertically downward, needs to be applied at the left end of the pipe to prevent it from pressing against the right pillar.

Answer

The force F, directed vertically downward, that needs to be applied at the left end of the pipe is 392 N.