Question

На Кінцях невагомого стержня довжиною 1м, що має вісь обертання, підвішені вантажі масами 1 і 4 кг. Стержень з вантажами перебуває в стані рівноваги в горизонтальному положенні. Визначити на якій відстані від точки підвісу меншого вантажу находиться вісь обертання стержня ============================================================ На концах невесомого стержня длиной 1м, имеющего ось вращения, подвешены грузы массами 1 и 4 кг. Стержень с грузами находится в состоянии равновесия в горизонтальном положении. Определить на каком расстоянии от точки подвеса меньшего груза находиться ось вращения стержня

Answer 1

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Answer 2

To determine the distance from the point of suspension of the smaller load to the axis of rotation of the rod, we can use the principle of moments. The principle of moments states that for an object in rotational equilibrium, the sum of the clockwise moments is equal to the sum of the counterclockwise moments.

Let's denote the distance from the point of suspension to the axis of rotation as 'x'. We can set up the following equation based on the principle of moments:

Clockwise moments = Counterclockwise moments

The clockwise moments are caused by the larger load (4 kg) and can be calculated as the product of its mass and the distance from the axis of rotation:

Clockwise moments = 4 kg * (1 m - x)

The counterclockwise moments are caused by the smaller load (1 kg) and can be calculated as the product of its mass and the distance from the axis of rotation:

Counterclockwise moments = 1 kg * x

Setting the clockwise moments equal to the counterclockwise moments, we have:

4 kg * (1 m - x) = 1 kg * x

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

4 kg * (1 m - x) = 1 kg * x

4 kg - 4 kg * x = 1 kg * x

4 kg = 5 kg * x

x = 4 kg / 5 kg

x = 0.8 m

Therefore, the axis of rotation of the rod is located at a distance of 0.8 meters from the point of suspension of the smaller load.

Please note that the above calculation assumes that the rod is massless and the gravitational force acts vertically downwards.