Question

In Exercise 9, what would the distance across the top of the worm thread have to be to make d equal to 0 inches?

Answer 1

When `d=0` inches the situation will be represented by the modified figure as shown above. The distance across the top of the worm thread then will be `PR`

Now `PR =2PQ= (2PQ)/(OQ)xxOQ`

`=>PR = (2PQ)/(OQ)xx(QC+CQ)`

`=>PR = (2PQ)/(OQ)xx(QC+(CQ)/(CN)xxCN)`

`=>PR = (2PQ)/(OQ)xx(CN+(CQ)/(CN)xxCN)`

`=>PR = (2PQ)/(OQ)xxCN(1+(CQ)/(CN))`

`=>PR = 2tanthetaxx0.75(1+csctheta)`

`=>PR = 1.5(tantheta+tanthetaxxcsctheta)`

`=>PR = 1.5(tantheta+sectheta)`

`=>PR = 1.5(tan15^@+sec15^@)~~1.95` inch