The maximum efficiency of screw jack is (when ϕ - angle of friction): 

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  1. \(\eta = \frac{{1 - sin\phi }}{{1 + sin\phi }} \)
  2. \(\eta = \frac{{1 + sin\phi }}{{1 - sin\phi }} \)
  3. \(\eta = \frac{{1 - tan\phi }}{{1 + tan\phi }} \)
  4. \(\eta = \frac{{1 + tan\phi }}{{1 - tan\phi }} \)

Answer (Detailed Solution Below)

Option 1 : \(\eta = \frac{{1 - sin\phi }}{{1 + sin\phi }} \)
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Detailed Solution

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Explanation:

Screw jack

  • A screw jack is a portable device consisting of a screw mechanism used to raise or lower the load. There are two types of jack Hydraulic and mechanical
  • A Hydraulic jack consists of a cylinder and piston mechanism. The movement of piston rod is used to raise or lower the load.
  • Mechanical jack can be either hand-operated or power-driven.   

The maximum efficiency of the screw jack is:

\(\eta = \frac{{1 - sin\phi }}{{1 + sin\phi }} \)

The maximum efficiency of screw jack is when helix angle α is

\(\alpha = 45^\circ- \frac{\phi }{2}\)

Additional Information

The screw used in screw jack:

  • The screw jack is intermittently used device and wear of thread is not an important consideration. Therefore instead of trapezoidal or V threads, the screw is provided with square threads.
  • Square threads have higher efficiency and provision can be made for self-locking arrangement.
  • When the condition of self-locking is fulfilled, the load itself will not turn the screw and descend down, unless the handle is rotated in reverse direction with some effort
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