Question

Человек стоит на льду. Площадь подошвы одного его ботинка равна 270 см2.Во сколько раз изменится давление человека на лёд, если он наденет коньки?Длина лезвия конька равна 21 см, а его ширина — 4 мм.пожалуйста помогите

Answer 1

Добрый день. Пользуясь основным уравнениям для давления P=F/S, не сложна наблюдать зависимость.Т.к масса человека не изменялась она сократилась в процессе преобразования

Answer 2

Calculation of Pressure Change

To calculate the change in pressure when a person stands on ice and then wears ice skates, we need to compare the pressure exerted by the person's shoe with the pressure exerted by the ice skate blade.

Let's break down the calculation step by step:

1. Calculate the pressure exerted by the person's shoe on the ice: - The area of one shoe sole is given as 270 cm². - The person's weight is not provided, so we'll assume a weight of 70 kg for this calculation. - Convert the area from cm² to m²: 270 cm² = 0.027 m². - Calculate the pressure using the formula: pressure = force / area. - The force exerted by the person is equal to their weight, which is 70 kg multiplied by the acceleration due to gravity (9.8 m/s²). - Substitute the values into the formula: pressure = (70 kg * 9.8 m/s²) / 0.027 m².

2. Calculate the pressure exerted by the ice skate blade on the ice: - The length of the ice skate blade is given as 21 cm. - The width of the ice skate blade is given as 4 mm, which is equivalent to 0.004 m. - Calculate the area of the ice skate blade by multiplying the length and width: area = 21 cm * 0.004 m = 0.084 m². - Calculate the pressure using the same formula as before: pressure = force / area. - The force exerted by the person wearing the ice skates is still the same, so we can reuse the value calculated earlier. - Substitute the values into the formula: pressure = (70 kg * 9.8 m/s²) / 0.084 m².

3. Calculate the ratio of the pressures: - Divide the pressure exerted by the ice skate blade by the pressure exerted by the person's shoe.

Let's perform the calculations:

1. Pressure exerted by the person's shoe on the ice: - Area of one shoe sole: 270 cm² = 0.027 m². - Weight of the person: 70 kg. - Pressure = (70 kg * 9.8 m/s²) / 0.027 m² = 255,925.93 Pa.

2. Pressure exerted by the ice skate blade on the ice: - Length of the ice skate blade: 21 cm = 0.21 m. - Width of the ice skate blade: 4 mm = 0.004 m. - Area of the ice skate blade: 0.21 m * 0.004 m = 0.00084 m². - Pressure = (70 kg * 9.8 m/s²) / 0.00084 m² = 823,809,523.81 Pa.

3. Ratio of the pressures: - Pressure exerted by the ice skate blade / Pressure exerted by the person's shoe = 823,809,523.81 Pa / 255,925.93 Pa = 3,218.75.

Therefore, if a person stands on ice and then wears ice skates, the pressure they exert on the ice will increase by a factor of approximately 3,218.75.