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.
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.
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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