Question

Сила, яка діе на кінець довшого плеча важеля, що перебуває у стані рівноваги, дорівнюе 150Н, а сила, яка діє на кінець коротшого плеча, становить 900 Н. Визначити довжину короткого плеча, якщо довше плече має довжину 1,2 м. Масою важеля можна знехтувати.​

Answer 1

Ответ: 0,2м

Объяснение:

Дано:

F1=150Н

F2=900Н

l1=1,2м

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l2-?

Правило рычага гласит: Рычаг находится в равновесии, если приложенные к нему силы обратно пропорциональны их плечам:. Из формулы, применив к ней свойство пропорции (произведение крайних членов пропорции равно произведению ее средних членов), можно получить такую формулу: F 1 l 1= F 2 l 2.

Отсюда l2=F1*l1/F2=150*1,2/900=0,2м

Answer 2

Calculation of the Shorter Arm Length in a Lever System

To determine the length of the shorter arm in a lever system, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point when the system is in equilibrium.

In this case, we have a lever system with two forces acting on it. The force acting on the longer arm is 150 N, and the force acting on the shorter arm is 900 N. We are given that the longer arm has a length of 1.2 m.

Let's assume that the shorter arm has a length of x meters. According to the principle of moments, the clockwise moment about the point of equilibrium is equal to the anticlockwise moment.

The clockwise moment is given by the product of the force (150 N) and the distance from the point of equilibrium to the force, which is 1.2 m.

The anticlockwise moment is given by the product of the force (900 N) and the distance from the point of equilibrium to the force, which is x meters.

Setting up the equation:

150 N * 1.2 m = 900 N * x

Simplifying the equation:

180 N·m = 900 N·m

Dividing both sides of the equation by 900 N:

180 N·m / 900 N = x

x = 0.2 m

Therefore, the length of the shorter arm in the lever system is 0.2 meters.