What is a screw jack? How does it work? Which principle of physics does it use? How to calculate effort required and efficiency of a screw jack?
The principle, on which a screw jack works is similar to that of an inclined plane. If one complete turn of a screw thread is imagined to be unwound, from the body of the screw jack and developed, it will form an inclined plane, as shown in Fig. 1.22.
From the geometry of the figure,
![Effort required in a Screw Jack Screw Jack](data:image/png;base64,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)
In a screw jack, the effort (P) required at the circumference of screw is same as discussed for inclined plane, i.e.
For raising the load, P = W tan (α + ϕ)
and for lowering the load, P = W tan (α - ϕ)
Notes:
1. When friction is neglected, then Ï• = 0. In that case
![](data:image/png;base64,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)
2. The efficiency of a screw jack is given by
![The efficiency of a screw jack The efficiency of a screw jack](data:image/png;base64,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)
3. The efficiency of a screw jack is maximum, when helix angle,
![Maximum efficiency of a screw jack Maximum efficiency of a screw jack](data:image/png;base64,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)
and the maximum efficiency is given by
![Maximum efficiency of a screw jack Maximum efficiency of a screw jack](data:image/png;base64,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)
The principle, on which a screw jack works is similar to that of an inclined plane. If one complete turn of a screw thread is imagined to be unwound, from the body of the screw jack and developed, it will form an inclined plane, as shown in Fig. 1.22.
From the geometry of the figure,
In a screw jack, the effort (P) required at the circumference of screw is same as discussed for inclined plane, i.e.
For raising the load, P = W tan (α + ϕ)
and for lowering the load, P = W tan (α - ϕ)
Notes:
1. When friction is neglected, then Ï• = 0. In that case
2. The efficiency of a screw jack is given by
3. The efficiency of a screw jack is maximum, when helix angle,
and the maximum efficiency is given by
NICE
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