Question

ДАМ МНОГО БАЛЛОВ До одного кінця стрижня масою 10 кг підвісили вантаж так, що стрижень перебуває в рівновазі в горизонтальному положенні, якщо його підперти на відстані 1/3 довжини стрижня від вантажу. Чому дорівнює вага вантажу? Відповідь надайте з одиницею вимірювання. Зробіть пояснювальний рисунок.​

Answer 1

To find the weight of the load in this scenario, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

In this case, the load is suspended from a rod, and the rod is supported at a distance of 1/3 of its length from the load. Let's assume the length of the rod is L.

Applying the principle of moments:

- Clockwise moments: The weight of the load multiplied by the distance from the support to the load, which is (1/3)L. - Anticlockwise moments: The weight of the rod multiplied by the distance from the support to the center of mass of the rod, which is (2/3)L.

Since the rod is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments. Therefore, we can write the equation:

(Weight of the load) * (1/3)L = (Weight of the rod) * (2/3)L

To find the weight of the load, we need to know the weight of the rod. The weight of the rod is equal to its mass multiplied by the acceleration due to gravity. In this case, the mass of the rod is 10 kg.

Calculating the weight of the rod:

The weight of the rod = (mass of the rod) * (acceleration due to gravity) = 10 kg * 9.8 m/s^2 = 98 N

Now, we can substitute the weight of the rod into the equation and solve for the weight of the load.

(Weight of the load) * (1/3)L = 98 N * (2/3)L

By canceling out the common factor of L, we get:

(Weight of the load) * (1/3) = 98 N * (2/3)

Simplifying further:

(Weight of the load) = 98 N * (2/3) / (1/3) = 98 N * 2 = 196 N

Therefore, the weight of the load is 196 N.

Explanation with a diagram:

Here is a diagram to help visualize the scenario:

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