# Homework Help: Simple Pulley Belt Question

1. Sep 2, 2008

### ur5pointos2sl

A narrow belt is used to drive a 20.00-cm diameter pulley from a 35.00-cm-diameter pulley. The centers of the two pulleys are 2.000 m apart. How long must the belt be if the pulleys rotate in the same direction? In opposite directions?

I am sure the solution to this problem is very simple, but I just cannot seem to figure out how to even begin this problem.Any help would be appreciated.

2. Sep 3, 2008

### spideyunlimit

I think you just need to find the hypotenuse using trigonometry.

3. Sep 3, 2008

### Redbelly98

Staff Emeritus
Solving this begins with drawing a picture of the wheels and belt.

4. Sep 3, 2008

### ur5pointos2sl

well of course that would be the obvious thing to do. Once i have it drawn I am guessing I need to form a right triangle? Simply by extending a tangent line from one pulley to the other on top and bottom? From here i am stuck. I know that the center is 2 cm but how do you calculate for the belt wrapping around the pulley itself? Would that be arc length or something?

5. Sep 3, 2008

### tiny-tim

Hi ur5pointos2sl!
Yes, that's arc-length!

6. Sep 4, 2008

### Redbelly98

Staff Emeritus
Okay, guess I took you too literally when you said you didn't know how to begin.

Pretty much. Draw simple shapes like right triangles, rectangles, and/or circles to figure things out. Yes, the length of belt portion wrapping around the pulley is an arc length; you'll need to figure out the angle involved using geometry and trig.