Question

Лыжник общая площадь подошв обуви которого S=450 см^2, массой m1=70кг с рюкзаком массой m2=20кг стоит на снегу на лыжах длинной l=1,8 м и шириной a=8 см каждая. Определите, на сколько возрастет давление лыжника на снег, если он снимет лыжи и рюкзак.

Answer 1

Дано:
S = 450 см^2 = 0.045 м^2
m1 = 70 кг
m2 = 20 кг
l = 1.8 м
a = 8 см = 0.08 м
p1 - ?
p2 - ?
Решение:
p = F/S; F = mg; S = la
F1 = 70 × 10 = 700 H
F2 = 20 × 10 = 200 H
S = 1.8 × 0.08 = 0.144 × 2 = 0.288 м^2
p1 = (700 + 200)/0.288 = 3125 Па - давление с рюкзаком на лыжах
р2 = 700/0.045 = 15555 Па - давление без рюкзака
1)15555 - 3125 = 12430 - на столько возрастет давление на снег
Ответ: на 12430 Па

Answer 2

Calculation of Pressure Increase

To determine the increase in pressure on the snow when the skier removes their skis and backpack, we need to calculate the initial pressure and compare it to the final pressure.

Given information: - Area of the skier's shoe soles, S = 450 cm^2 - Mass of the skier, m1 = 70 kg - Mass of the backpack, m2 = 20 kg - Length of the skis, l = 1.8 m - Width of each ski, a = 8 cm

Initial Pressure Calculation

The initial pressure exerted by the skier on the snow can be calculated using the formula:

Pressure = Force / Area

To calculate the force exerted by the skier on the snow, we need to consider the weight of the skier and the backpack. The weight is given by:

Weight = Mass * Gravity

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

The total weight of the skier and the backpack is:

Total Weight = (Mass of Skier + Mass of Backpack) * Gravity

The force exerted by the skier on the snow is equal to the total weight.

Now, we can calculate the initial pressure:

Initial Pressure = Force / Area

Final Pressure Calculation

When the skier removes their skis and backpack, the area in contact with the snow decreases. The final pressure can be calculated using the same formula:

Final Pressure = Force / Area

where the area is the area of the skier's shoe soles, S.

Calculation of Pressure Increase

To determine the increase in pressure, we need to compare the initial pressure with the final pressure:

Pressure Increase = Final Pressure - Initial Pressure

Let's calculate the pressure increase:

Step 1: Calculate the total weight of the skier and the backpack: Total Weight = (Mass of Skier + Mass of Backpack) * Gravity

Step 2: Calculate the initial pressure: Initial Pressure = Total Weight / Area

Step 3: Calculate the final pressure: Final Pressure = Total Weight / S

Step 4: Calculate the pressure increase: Pressure Increase = Final Pressure - Initial Pressure

Now, let's plug in the given values and calculate the pressure increase.

Given: - S = 450 cm^2 - m1 = 70 kg - m2 = 20 kg - l = 1.8 m - a = 8 cm

Converting units: - S = 450 cm^2 = 0.045 m^2 - a = 8 cm = 0.08 m

Calculations: Step 1: Calculate the total weight of the skier and the backpack: Total Weight = (70 kg + 20 kg) * 9.8 m/s^2

Step 2: Calculate the initial pressure: Initial Pressure = Total Weight / Area

Step 3: Calculate the final pressure: Final Pressure = Total Weight / S

Step 4: Calculate the pressure increase: Pressure Increase = Final Pressure - Initial Pressure

Let's calculate the values:

Step 1: Calculate the total weight of the skier and the backpack: Total Weight = (70 kg + 20 kg) * 9.8 m/s^2 = 882 N

Step 2: Calculate the initial pressure: Initial Pressure = 882 N / 0.045 m^2

Step 3: Calculate the final pressure: Final Pressure = 882 N / 0.045 m^2

Step 4: Calculate the pressure increase: Pressure Increase = Final Pressure - Initial Pressure

Now, let's calculate the values:

Step 1: Calculate the total weight of the skier and the backpack: Total Weight = (70 kg + 20 kg) * 9.8 m/s^2 = 882 N

Step 2: Calculate the initial pressure: Initial Pressure = 882 N / 0.045 m^2 = 19600 Pa

Step 3: Calculate the final pressure: Final Pressure = 882 N / 0.045 m^2 = 19600 Pa

Step 4: Calculate the pressure increase: Pressure Increase = Final Pressure - Initial Pressure = 0 Pa

Therefore, when the skier removes their skis and backpack, there will be no increase in pressure on the snow. The pressure will remain the same as the initial pressure.

Please note that the calculations provided are based on the given information and assumptions.