Question

Горизонтальный однородный стержень длиной 60 см и массой 200 г имеет точку опоры, находящуюся на расстоянии х от левого конца стержня. К концам стержня на невесомых нитях подвешены грузы: слева – массой 250 г и справа – массой 50 г. Грузы и стержень находятся в равновесии. Чему равно расстояние х? Выберите один ответ: 0,20 м 0,28 м 0,38 м 0,08 м 0,18 м

Answer 1

Ответ:

0,18 м

Объяснение:

Изобразим все силы, действующие на стержень (см. рисунок). Так как стержень находится в равновесии, сумма всех моментов, действующих на стержень относительно точки опоры равна нулю:

$\displaystyle m_1gx-Mg(\frac{L}{2}-x )-m_2g(L-x)=0$

$0.25*10*x-0.2*10*(0.3-x)-0.05*10*(0.6-x)=0$

$\displaystyle 5x=0.9$

$\displaystyle x=0.18$ м.

Answer 2

I can answer your question in detail. The horizontal uniform rod of length 60 cm and mass 200 g has a support point located at a distance x from the left end of the rod. To the ends of the rod, weights are suspended on weightless threads: on the left - with a mass of 250 g and on the right - with a mass of 50 g. The weights and the rod are in equilibrium. What is the distance x? Choose one answer: 0.20 m 0.28 m 0.38 m 0.08 m 0.18 m

To solve this problem, we need to apply the principle of moments, which states that the sum of the moments of all forces acting on a body about any point is zero if the body is in equilibrium. A moment is the product of a force and its perpendicular distance from the point.

Let us choose the support point as the point about which we calculate the moments. The forces acting on the rod are:

- The weight of the rod, which acts at its center of mass, that is, at a distance of 30 cm from either end. - The weight of the left load, which acts at a distance of x from the support point. - The weight of the right load, which acts at a distance of (60 - x) cm from the support point.

The weight of an object is equal to its mass times the acceleration due to gravity, which we can take as 9.8 m/s^2^. Therefore, we have:

- The weight of the rod: W_r = 0.2 kg * 9.8 m/s^2 = 1.96 N - The weight of the left load: W_l = 0.25 kg * 9.8 m/s^2 = 2.45 N - The weight of the right load: W_r = 0.05 kg * 9.8 m/s^2 = 0.49 N

The moment of a force is positive if it tends to rotate the body clockwise about the point, and negative if it tends to rotate it counterclockwise. Therefore, we have:

- The moment of the weight of the rod: M_r = -W_r * 0.3 m = -0.588 Nm - The moment of the weight of the left load: M_l = -W_l * x - The moment of the weight of the right load: M_r = W_r * (0.6 - x)

According to the principle of moments, we have:

M_r + M_l + M_r = 0

Substituting the values, we get:

-0.588 - 2.45x + 0.49(0.6 - x) = 0

Simplifying, we get:

2.94x = 1.176

Dividing by 2.94, we get:

x = 0.4 m

Therefore, the correct answer is none of the given options, as x is equal to 0.4 m.

I hope this explanation was helpful for you.

: [Moment (physics) - Wikipedia] : [Principle Of Moments | Definition & Examples | GCSE Physics]