Question

Груз массой m1=200 г подвешен к одному из концов однородного алюминиевого стержня, а на расстоянии d=20 см от него к стержню подвешен второй груз массой m2=100 г, как показано на рисунке. На каком расстоянии от первого груза нужно расположить опору, чтобы стержень покоился в горизонтальном положении? Длина стержня l=1 м, площадь поперечного сечения стержня S=1 см2, плотность алюминия ρ=2700 кг/м3. Ответ выразите в см, округлив до целого числа.

Answer 1

Ответ:

38

Объяснение:

это точно

решение долго писать

Answer 2

Problem Analysis

We are given a problem where a mass of m1 = 200 g is suspended from one end of a uniform aluminum rod, and at a distance of d = 20 cm from the rod, another mass of m2 = 100 g is suspended. We need to determine the distance from the first mass where a support should be placed in order for the rod to be in a horizontal position. The length of the rod is l = 1 m, the cross-sectional area of the rod is S = 1 cm^2, and the density of aluminum is ρ = 2700 kg/m^3.

Solution

To solve this problem, we can use the principle of moments. The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.

Let's assume that the support is placed at a distance x from the first mass. The clockwise moment due to the first mass is m1 * g * (l - x), where g is the acceleration due to gravity. The counterclockwise moment due to the second mass is m2 * g * (d + x). Since the rod is in a horizontal position, the sum of the clockwise moments and the sum of the counterclockwise moments must be equal.

Setting up the equation:

m1 * g * (l - x) = m2 * g * (d + x)

Simplifying the equation:

m1 * (l - x) = m2 * (d + x)

Expanding the equation:

m1 * l - m1 * x = m2 * d + m2 * x

Rearranging the equation:

m1 * l - m2 * d = (m1 + m2) * x

Solving for x:

x = (m1 * l - m2 * d) / (m1 + m2)

Now we can substitute the given values and calculate the distance x.

Calculation

Given: m1 = 200 g = 0.2 kg m2 = 100 g = 0.1 kg l = 1 m d = 20 cm = 0.2 m

Using the formula:

x = (m1 * l - m2 * d) / (m1 + m2)

Substituting the values:

x = (0.2 * 1 - 0.1 * 0.2) / (0.2 + 0.1)

Simplifying the expression:

x = (0.2 - 0.02) / 0.3

x = 0.18 / 0.3

x ≈ 0.6 m

Answer

The support should be placed at a distance of approximately 0.6 m from the first mass in order for the rod to be in a horizontal position.