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

length of the belt. Round your answer to the nearest hundredth.​

A rubber belt connects the two flywheels shown. Find the total length of the belt-example-1
User Sznrbrt
by
3.8k points

2 Answers

3 votes

Answer:

Total length = 29.42 in

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

==========================================

Total Length: 2*Lc + 2*Sc

==========================================

- 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

User Rwb
by
4.1k points
4 votes

Answer:


L\approx 29.43\,in

Explanation:

The total length of the belt is:


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


L\approx 29.43\,in

User Mounir Bkr
by
3.7k points