55_Problem CHAPTER 10

55_Problem CHAPTER 10 - PROBLEM 10.50 Derive an expression...

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Unformatted text preview: PROBLEM 10.50 Derive an expression for the mechanical efficiency of the jack discussed in Section 8.6. Show that if the jack is to be self-locking, the mechanical efficiency cannot exceed 1 . 2 SOLUTION Recall Figure 8.9a. Draw force triangle Q = W tan ( + s ) y = x tan so that y = x tan Input work = Q x = W tan ( + s ) x Output work = W y = W ( x ) tan Efficiency: = W tan x ; W tan ( + s ) x = tan tan ( + s ) From page 432, we know the jack is self-locking if s Then so that From above + s 2 tan ( + s ) tan 2 = tan tan ( + s ) It then follows that tan 2 = tan 1 - tan 2 2 tan tan tan 2 But 2 tan 1 - tan 2 Then ( ) = 1 - tan 2 2 1 2 ...
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