Question

Длина кирпича в 2 раза больше его ширины, а ширина — в 2 раза больше толщины. Сравните наибольшее (Pmax) и наименьшее (Pmin) значения давления, которое может оказывать этот кирпич на горизонтальную поверхность.

Answer 1

Pmax - 4 pmin

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Answer 2

Calculating Pressure Exerted by the Brick

The pressure exerted by the brick on a horizontal surface can be calculated using the formula:

Pressure (P) = Force (F) / Area (A)

Where: - Force (F) is the weight of the brick acting vertically downwards. - Area (A) is the area of contact between the brick and the horizontal surface.

Finding the Maximum and Minimum Pressure

Given that the length of the brick is twice its width, and the width is twice the thickness, we can calculate the maximum and minimum pressure the brick can exert on a horizontal surface.

Let's denote: - Length (L) = 2x - Width (W) = x - Thickness (T) = x/2

Calculating the Area of Contact

The area of contact between the brick and the horizontal surface can be calculated as: Area (A) = Length (L) * Width (W)

Substituting the given values: Area (A) = 2x * x = 2x^2

Calculating the Force Exerted by the Brick

The force exerted by the brick can be calculated as: Force (F) = Mass (M) * Acceleration due to gravity (g)

Given that the mass of the brick is directly proportional to its volume, and the volume can be calculated as: Volume = Length (L) * Width (W) * Thickness (T)

Substituting the given values: Volume = 2x * x * (x/2) = x^2

The mass of the brick can be assumed to be directly proportional to its volume.

Comparing the Maximum and Minimum Pressure

To compare the maximum and minimum pressure, we need to calculate the maximum and minimum force exerted by the brick and then use these values to calculate the corresponding maximum and minimum pressure.