Question

Определите период обращения колеса автомобиля при скорости 72 км/ч, если радиус колеса 40 см.

Answer 1

Дано:
V = 72 км/ч = 20 м/с
R = 40 см = 0,40 м

Длина окружности:
С = 2·π·R = 2·π·0,40 = 0,80·π
Период:

T = C/V = 0,80·π / 20 ≈ 0,13 с

Период равен 0,13 секунд

Answer 2

Calculation of the Wheel Revolution Period

To determine the period of revolution of a car wheel at a speed of 72 km/h, we need to consider the circumference of the wheel and the speed at which it is rotating.

The circumference of a circle can be calculated using the formula:

Circumference = 2 * π * radius

Given that the radius of the car wheel is 40 cm, we can calculate the circumference as follows:

Circumference = 2 * π * 40 cm

To convert the circumference to meters, we divide it by 100:

Circumference = (2 * π * 40) / 100 meters

Now, we need to calculate the time it takes for the wheel to complete one revolution at a speed of 72 km/h. To do this, we can use the formula:

Time = Distance / Speed

Since the distance covered by the wheel in one revolution is equal to the circumference of the wheel, we can substitute the circumference into the formula:

Time = Circumference / Speed

Substituting the values we calculated earlier:

Time = [(2 * π * 40) / 100] / 72 km/h

To convert the speed from km/h to m/s, we divide it by 3.6:

Time = [(2 * π * 40) / 100] / (72 / 3.6) m/s

Simplifying the equation:

Time = [(2 * π * 40) / 100] / (72 / 3.6) m/s

Now, let's calculate the value:

Time = [(2 * 3.14159 * 40) / 100] / (72 / 3.6) m/s

Using a calculator, we find that the time it takes for the wheel to complete one revolution at a speed of 72 km/h is approximately 0.125 seconds.

Please note that this calculation assumes that the car is moving in a straight line and that there are no other factors affecting the rotation of the wheel.