Question

ведущая шестерня велосипеда имеет 42 зубца , а ведомая шестерня имеет 28 зубцов 1) сколько оборотов сделает ведомая шестерня, в то время как ведущая шестерня сделает 38 оборотов 2) сколько оборотов должна сделать ведущая шесТерня, чтобы ведомая шестерня совершила 45 оборотов?

Answer 1

Calculation of Gear Ratios

To answer your questions about the number of rotations made by the gears, we need to calculate the gear ratios. The gear ratio is the ratio of the number of teeth on the driving gear (the one connected to the pedals) to the number of teeth on the driven gear (the one connected to the wheel).

1) How many rotations will the driven gear make while the driving gear makes 38 rotations?

To calculate this, we can use the formula:

Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Driving Gear

In this case, the number of teeth on the driving gear (the leading gear) is 42, and the number of teeth on the driven gear (the driven gear) is 28.

So the gear ratio is:

Gear Ratio = 28 / 42 = 2/3

This means that for every 2 rotations of the driving gear, the driven gear will make 3 rotations.

Therefore, if the driving gear makes 38 rotations, the driven gear will make:

Number of Rotations of Driven Gear = (38 rotations) * (3 rotations / 2 rotations) = 57 rotations

So the driven gear will make 57 rotations while the driving gear makes 38 rotations.

2) How many rotations should the driving gear make for the driven gear to make 45 rotations?

To calculate this, we can rearrange the gear ratio formula:

Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Driving Gear

In this case, the number of teeth on the driven gear is 28, and the number of teeth on the driving gear is 42.

So the gear ratio is:

Gear Ratio = 28 / 42 = 2/3

To find the number of rotations of the driving gear, we can rearrange the formula:

Number of Rotations of Driving Gear = (Number of Rotations of Driven Gear) * (Number of Teeth on Driving Gear / Number of Teeth on Driven Gear)

Substituting the given values, we get:

Number of Rotations of Driving Gear = 45 rotations * (42 teeth / 28 teeth) = 67.5 rotations

Therefore, the driving gear should make approximately 67.5 rotations for the driven gear to make 45 rotations.

Please note that these calculations assume ideal conditions and do not take into account any losses due to friction or other factors that may affect the actual number of rotations.