# Homework Help: How do you find how far a belt travels using diameter and rps

1. Apr 20, 2010

### 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?

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

3. 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.

2. Apr 21, 2010

### tiny-tim

Welcome to PF!

Hi daniellen! Welcome to PF!
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.

3. Apr 22, 2010

### daniellen

Re: Welcome to PF!

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)

4. Apr 23, 2010

### tiny-tim

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 … ?

5. Apr 23, 2010

### daniellen

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

6. Apr 24, 2010

### tiny-tim

Stitches per minute = revolutions per minute …
and so … ?