A crossed belt connects a 10-centimeter pulley on an electric motor with a 20-centimeter

Chapter 5, Problem 66

(choose chapter or problem)

Mechanical Engineering A crossed belt connects a 10-centimeter pulley on an electric motor with a 20-centimeter pulley on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

(a) Determine the number of revolutions per minute of the saw.

(b) How does crossing the belt affect the saw in relation to the motor?

(c) Let L be the total length of the belt. Write L as a function of \(\phi\), where \(\phi\) is measured in radians. What is the domain of the function? (Hint: Add the lengths of the straight sections of the belt and the length of the belt around each pulley.)

(d) Use a graphing utility to complete the table.

(e) As \(\phi\) increases, do the lengths of the straight sections of the belt change faster or slower than the lengths of the belts around each pulley?

(f) Use the graphing utility to graph the function over the appropriate domain.

Text Transcription:

phi