Calculating Belt Length for Pulley Rotation

[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.

 

[spideyunlimit]

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

 

[Redbelly98]

... I just cannot seem to figure out how to even begin this problem.

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

 

[ur5pointos2sl]

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

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?

 

[tiny-tim]

Hi ur5pointos2sl!

… how do you calculate for the belt wrapping around the pulley itself? Would that be arc length or something?

Yes, that's arc-length!

 

[Redbelly98]

well of course that would be the obvious thing to do.

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

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?

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.