Question

A rubber belt connects the two flywheels shown. Find the total

Answer 1

Answer:

Total length = 29.42 in

Step-by-step explanation:

Solution:-

Denote:

- The center to center length Lc = 10 in

- The diameter of the flywheel, d = 3 in

- We see that the length of the belt can be broken down into 4 section.

          Upper horizontal ( Center to Center ) = Lc

          Lower horizontal ( Center to Center ) = Lc

          Right half wheel curves surface = Sc

          Left half wheel curves surface = Sc

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Total Length:                2*Lc + 2*Sc

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- To determine the length of the belt wrapped around the curved surface of the flywheel. Here, we shall assume a wrap angle = 180°.  

- The circumference of a circle ( C ) with diameter d is given below:

                      C = π*d

We will use half of the circumference to be equal to Sc:

                     Sc = 0.5*C = 0.5* π*d

                     Sc = 0.5*π*(3)

                     Sc = 4.71238 in

- Now we can determine the total length of the belt used :

                  Total Length = 2*Lc + 2*Sc

                                         = 2*(10) + 2*(4.71238)

                                         = 29.4247 in

- Round off to nearest hundredth by truncating 3rd decimal place and onwards.

                   Total length = 29.42 in

Answer 2

Answer:

$L\approx 29.43\,in$

Step-by-step explanation:

The total length of the belt is:

$L = 2\pi\cdot (1.5\,in) + 20\,in$

$L\approx 29.43\,in$