Part C. 1. Forces of 2 N and 18 N act on the ends of a lever. The length of the lever is 1 m. Where is the fulcrum if the lever is in equilibrium? (The weight of the lever is negligible)

Solution:

This is a problem about levers in equilibrium. The condition for equilibrium of a lever is that the moments of the forces acting on it must be equal.

Let \( F_1 = 2 \) N and \( F_2 = 18 \) N be the forces acting on the ends of the lever. Let \( l_1 \) and \( l_2 \) be the distances from the fulcrum to the points where the forces are applied, respectively.

The condition for equilibrium is \( F_1 \cdot l_1 = F_2 \cdot l_2 \).

We are also given that the total length of the lever is 1 m, so \( l_1 + l_2 = 1 \) m.

We have two equations:

1. \( 2 \cdot l_1 = 18 \cdot l_2 \)
2. \( l_1 + l_2 = 1 \)

From the first equation, we can express \( l_1 \) in terms of \( l_2 \): \( l_1 = \frac{18}{2} \cdot l_2 = 9 \cdot l_2 \).

Substitute this into the second equation:

\( 9 \cdot l_2 + l_2 = 1 \)

\( 10 \cdot l_2 = 1 \)

\( l_2 = \frac{1}{10} = 0.1 \) m.

Now find \( l_1 \):

\( l_1 = 1 - l_2 = 1 - 0.1 = 0.9 \) m.

The fulcrum should be located at a distance of 0.9 m from the point where the 2 N force is applied, and 0.1 m from the point where the 18 N force is applied.

Ответ: Точка опоры находится на расстоянии 0.9 м от силы 2 Н и 0.1 м от силы 18 Н.