Question

Два шкива соединены приводным ремнем (рис . 1.6). Длина окружности большего шкива 54 см,а меньшего-36 cм. Больший шкив делает 30 оборотов в минуту . Сколько оборотов в минуту делает меньший шкив ?

Answer 1

Составим пропорцию

54 см - 30 оборотов
36 см -  х оборотов
Обратная зависимость, с увеличением длины окружности количество оборотов УМЕНЬШАЕТСЯ

$\frac{54}{36}$ = $\frac{x}{30}$

По основному свойству пропорции: произведение крайних = произведению средних

36х = 54 * 30

х = $\frac{54*30}{36}$

x = 45 оборотов

Answer 2

Calculation of the Number of Revolutions per Minute of the Smaller Pulley

To calculate the number of revolutions per minute (RPM) of the smaller pulley, we can use the relationship between the circumferences of the two pulleys and the RPM of the larger pulley.

Let's denote the circumference of the larger pulley as C1 (54 cm) and the circumference of the smaller pulley as C2 (36 cm). We are given that the larger pulley makes 30 revolutions per minute.

The relationship between the circumferences and the number of revolutions per minute is as follows:

C1 / C2 = RPM2 / RPM1

Where: - C1 is the circumference of the larger pulley - C2 is the circumference of the smaller pulley - RPM1 is the number of revolutions per minute of the larger pulley - RPM2 is the number of revolutions per minute of the smaller pulley

Plugging in the given values, we have:

54 cm / 36 cm = RPM2 / 30 RPM

Simplifying the equation, we find:

RPM2 = (54 cm / 36 cm) * 30 RPM

Now, let's calculate the value of RPM2:

RPM2 = (54 cm / 36 cm) * 30 RPM

RPM2 = 1.5 * 30 RPM

RPM2 = 45 RPM

Therefore, the smaller pulley makes 45 revolutions per minute.

Please let me know if there's anything else I can help you with!