Question

Доска опирается на подставку,находящуюся на расстоянии l/4 длины доски.Для удержания доски в равновесии в горизонтальном положении к ее короткому концу необходимо приложить силу 50Н Чему равна масса доски?

Answer 1

Из условия равновесия

F1*d1=m*g*d2
d1=d2=L/4
F1=m*g
m=F1/g=50/10=5 кг

Answer 2

Calculation of the Mass of the Board

To determine the mass of the board, we can use the principle of torque equilibrium. The torque exerted by the force applied at the short end of the board must be balanced by the torque exerted by the weight of the board acting at its center of mass.

The torque exerted by a force is given by the formula:

Torque = Force x Distance

In this case, the force applied at the short end of the board is 50 N, and the distance from the force to the center of mass is l/4, where l is the length of the board.

The torque exerted by the weight of the board is given by the formula:

Torque = Weight x Distance

The weight of the board can be calculated using the formula:

Weight = Mass x Gravity

where gravity is the acceleration due to gravity, approximately 9.8 m/s^2.

To find the mass of the board, we can equate the torques:

Force x Distance = Weight x Distance

Simplifying the equation:

Force = Weight

50 N = Mass x Gravity

Solving for mass:

Mass = 50 N / Gravity

Now we can calculate the mass of the board using the given force of 50 N.

Calculation:

Using the value of gravity as 9.8 m/s^2, we can calculate the mass of the board:

Mass = 50 N / 9.8 m/s^2

Mass ≈ 5.1 kg

Therefore, the mass of the board is approximately 5.1 kg.

Please note that the above calculation assumes a uniform distribution of mass along the length of the board and neglects any other external forces or factors that may affect the equilibrium.