• November 19th 2009, 01:41 AM
deltaxray
A flat belt is wrapped around two pulleys of diameter 10cm and 16cm seperated by a distance of 26cm as shown below.
Find the exact length of the belt.

Thanks guys.

http://img5.imageshack.us/img5/6594/54188893.jpg
• November 19th 2009, 04:24 AM
earboth
Quote:

Originally Posted by deltaxray
A flat belt is wrapped around two pulleys of diameter 10cm and 16cm seperated by a distance of 26cm as shown below.
Find the exact length of the belt.

Thanks guys.

http://img5.imageshack.us/img5/6594/54188893.jpg

I'm not sure what you meant by "distance of 26 cm":
- Is this the distance between the centres?
- Is this the clear space between the pulleys?

I've attached a correct construction of the inner common tangent of 2 circles.

You are dealing with 2 similar right triangles. The ratio of distances of these triangles depends of the ratio of the two radii.
• November 20th 2009, 06:28 AM
aidan
Quote:

Originally Posted by deltaxray
A flat belt is wrapped around two pulleys of diameter 10cm and 16cm seperated by a distance of 26cm as shown below.
Find the exact length of the belt.

Thanks guys.

http://img5.imageshack.us/img5/6594/54188893.jpg

Let r be the radius of the smaller pulley.
Let R be the radius of the larger pulley.
Let s be the smallest distance between the edges of the pulleys (r+s+R = distance be pulley centers).
Let $\theta$ be the acute angle where the belts 'intersect' -- theta in RADIANS.

$\theta = 2 \cdot arcsin \left( \dfrac{R+r}{R+s+r}\right)$

PerimeterLength = $(r+R)(\pi+\theta) + 2\sqrt{(R+s+r)^2 - (R+r)^2}$

Substitute your specific values into the equation.

.