How do you find how far a belt travels using diameter and rps

[daniellen]

the foot operated sewing machine shown below has a driver pulley which is 30cm in diameter and is attached by a belt to a sewing pulley with a 5cm diameter. The sewing machine makes one stitch for each revolution of its sewing pulley.
a. The driver pulley is turned easily at one revolution per second.
-how many stitches does the machine make in 10 minutes?
-how far would the belt travel in 10 minutes?
b. if the foot pedal(driver) was replaced by an electric motor with a pulley of diamater 1.5cm, how fast would it need to turn to duplicate the same sewing rate?

Homework Equations

I'm not sure what to put here, sorry.

The Attempt at a Solution

for A, I answered: the driver makes 600 rotations per minute. 600*5= 3.000
and for the rest I have no idea how to complete because I was absent for the explanation.

 

[tiny-tim]

Welcome to PF!

Hi daniellen! Welcome to PF!

a. The driver pulley is turned easily at one revolution per second.
-how many stitches does the machine make in 10 minutes?
-how far would the belt travel in 10 minutes?
b. if the foot pedal(driver) was replaced by an electric motor with a pulley of diamater 1.5cm, how fast would it need to turn to duplicate the same sewing rate?
…
for A, I answered: the driver makes 600 rotations per minute. 600*5= 3.000
and for the rest I have no idea how to complete because I was absent for the explanation.

Why *5 ?

The important point is that the belt goes at the same speed as the circumference of every pulley it's attached to (because it's not slipping) …

if it's attached to two pulleys, then their rotations (rpm) have to be such that their circumferences both move at the same speed (cm/s).

Try again. ​

 

[daniellen]

I did 5 because it is the diameter but I was not really sure.
So then would you find the circumference of the driver and then multiply it by 600o(because it the driver makes 1 rotation per second and its asking about 10 minutes)

Hi daniellen! Welcome to PF! :smile



Why *5 ?

The important point is that the belt goes at the same speed as the circumference of every pulley it's attached to (because it's not slipping) …

if it's attached to two pulleys, then their rotations (rpm) have to be such that their circumferences both move at the same speed (cm/s).

Try again. ​

 

[tiny-tim]

Hi daniellen!

(just got up :zzz: …)

I did 5 because it is the diameter but I was not really sure.
So then would you find the circumference of the driver and then multiply it by 600o(because it the driver makes 1 rotation per second and its asking about 10 minutes)

No. As I said …

The important point is that the belt goes at the same speed as the circumference of every pulley it's attached to (because it's not slipping) …

if it's attached to two pulleys, then their rotations (rpm) have to be such that their circumferences both move at the same speed (cm/s).

So if the two circumferences have the same speed, then the ratio of their rpms must be … ?

 

[daniellen]

the ratios would be six. so how do I implement that into finding how many stitches for 10 minutes and the belt?

Hi daniellen!

(just got up :zzz: …)


No. As I said …


So if the two circumferences have the same speed, then the ratio of their rpms must be … ?

 

[tiny-tim]

So if the two circumferences have the same speed, then the ratio of their rpms must be … ?

the ratios would be six. so how do I implement that into finding how many stitches for 10 minutes and the belt?

Stitches per minute = revolutions per minute …

The sewing machine makes one stitch for each revolution of its sewing pulley.

and so … ?