A belt is stretched tightly over two wheels having a radii of 1 and 5 inches, respectively. If the center of the wheels...?
are 8 inches apart, what is the total length of the straight sections of the belt?
- Ian HLv 74 weeks agoFavorite Answer
Look at the very helpful second diagram in the link given by RealPro
but replace 5cm, 3cm 14 cm by 5 inches, 1 inch, 8 inches
One straight section is given by L =√[8^2 – (5 – 1)^2] = 2√(7) inches
- Wayne DeguManLv 74 weeks ago
Refer to the 'rough' sketch below.
The belt touches the circumference of each wheel at points A and B. The lengths make up a trapezium. The parallel sides are the radii of 1 inch and 5 inches. The distance between them is AB and the slant side has length 8 inches.
From this, a right triangle is evident
so, using Pythagoras' theorem we have:
8² = (AB)² + (5 - 1)²
so, 64 = (AB)² + 16
=> (AB)² = 48
Hence, AB = √48 => 6.93 inches
so, straight sections total 2 x 6.93 = 13.9 inches
- RealProLv 74 weeks ago
Do you have a question?
r1 = 5 in
r2 = 1 in
d = 8 in
2sqrt( d^2 - (r1-r2)^2 ) + 2pi r1 + 2(r2-r1)arccos( (r1-r2)/d ) = 36.89 in
Output of arccos needs to be in radians.