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

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- Nov 19th 2009, 01:41 AMdeltaxrayRadian question
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 - Nov 19th 2009, 04:24 AMearboth
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. - Nov 20th 2009, 06:28 AMaidan
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 $\displaystyle \theta$ be the acute angle where the belts 'intersect' -- theta in RADIANS.

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

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

Substitute your specific values into the equation.

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