Question

Толщина льда на реке такова, что он выдерживает давление 40 кПа. Пройдет ли по льду трактор массой 5,4 т, если он опирается на гусеницы общей площадью 1,5м2 (считать g = 9,8 Н/кг)?

Answer 1

Дано:                              Решение:

m=5,4т=5400кг             p=$\frac{F}{S}$; F=mg;

S=1,5$m^{2}$     F=5400кг*9,8Н/кг=52920Н;

g=9,8 Н/кг                      р=52920Н/1,5$m^{2}$=35280Па=35,28кПа;

Найти: р                         35,28кПа<40кПа => пройдет.

                                        Ответ: да, пройдет.

Answer 2

Calculation of Pressure Exerted by the Tractor on the Ice

To determine whether the tractor with a mass of 5.4 tons can pass over the ice, we need to calculate the pressure exerted by the tractor on the ice surface. The formula for pressure is:

Pressure = Force / Area

In this case, the force is the weight of the tractor, and the area is the total area of the tracks in contact with the ice.

Given: - Tractor mass = 5.4 tons - Area of tracks = 1.5 m^2 - Acceleration due to gravity (g) = 9.8 N/kg

To calculate the force exerted by the tractor, we need to convert the mass from tons to kilograms:

Tractor mass = 5.4 tons * 1000 kg/ton = 5400 kg

Now we can calculate the force:

Force = Tractor mass * g = 5400 kg * 9.8 N/kg

To calculate the pressure, we divide the force by the area:

Pressure = Force / Area

Let's calculate the pressure using the given values:

Pressure = (5400 kg * 9.8 N/kg) / 1.5 m^2

Now we can calculate the pressure:

Pressure = 35280 N / 1.5 m^2

Calculation of Pressure in kilopascals (kPa)

To convert the pressure from newtons per square meter (N/m^2) to kilopascals (kPa), we divide the pressure by 1000:

Pressure in kPa = Pressure / 1000

Let's calculate the pressure in kilopascals:

Pressure in kPa = 35280 N / 1.5 m^2 / 1000

Now we can calculate the pressure in kilopascals:

Pressure in kPa = 23.52 kPa

Conclusion

The pressure exerted by the tractor on the ice is approximately 23.52 kilopascals (kPa). Based on the given information that the ice can withstand a pressure of 40 kPa, the tractor should be able to pass over the ice safely, as the pressure exerted by the tractor is below the maximum limit of 40 kPa.

Please note that this calculation assumes ideal conditions and does not take into account other factors that may affect the stability of the ice, such as its thickness, quality, and any potential weak spots. It is always important to exercise caution and ensure the ice is safe before attempting to drive a vehicle on it.