Question

Доска массой 10 кг лежит на двух бревнах,расстояние между которыми 1 м. На первое бревно доска давит с силой 40 Н. С какой силой она давит на второе бревно?На каком расстоянии от первого бревна находиться центр тяжести доски, если он совпадает с серединой доски?

Answer 1

Общая сила тяжести равна: 10*10=100Н
Отсюда, на второе бревно доска давит с силой 100-40=60 Н

Answer 2

Problem Analysis

We have a board with a mass of 10 kg lying on two logs, with a distance of 1 m between them. The board exerts a force of 40 N on the first log. We need to determine the force exerted by the board on the second log and the distance of the center of gravity of the board from the first log.

Force Exerted on the Second Log

To find the force exerted by the board on the second log, we can use the principle of equilibrium. Since the board is not accelerating vertically, the sum of the vertical forces acting on it must be zero. The force exerted by the first log on the board is equal in magnitude and opposite in direction to the force exerted by the board on the first log. Therefore, the force exerted by the board on the second log is also 40 N.

The force exerted by the board on the second log is 40 N.

Distance of the Center of Gravity from the First Log

To find the distance of the center of gravity of the board from the first log, we can use the principle of moments. The sum of the moments about any point must be zero for the board to be in rotational equilibrium. Let's choose the first log as the reference point.

The moment exerted by the force of 40 N on the first log is given by:

Moment = Force x Distance

Since the force is 40 N and the distance between the logs is 1 m, the moment exerted by the force on the first log is:

Moment = 40 N x 1 m = 40 Nm

To maintain rotational equilibrium, the moment exerted by the weight of the board (10 kg) must be equal and opposite to the moment exerted by the force on the first log. The weight of the board can be calculated using the formula:

Weight = Mass x Gravity

Where the mass is 10 kg and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the board is:

Weight = 10 kg x 9.8 m/s^2 = 98 N

To find the distance of the center of gravity from the first log, we can rearrange the equation for the moment:

Moment = Force x Distance

Rearranging for the distance:

Distance = Moment / Force

Substituting the values:

Distance = 40 Nm / 98 N ≈ 0.408 m

The center of gravity of the board is approximately 0.408 m from the first log.

Summary

To summarize: - The force exerted by the board on the second log is 40 N. - The center of gravity of the board is approximately 0.408 m from the first log.

Please let me know if you need any further clarification.