# Deriving the Expression for the Efficiency of Screw Jack

**Efficiency of a Screw Jack - may be defined as the ratio between its input effort which is applied at the lever end to the magnitude of work done or the weight lifted by the screw jack device.
Analyzing the standard equation which is given as,
P = W tan (alpha + phi)
Where P = effort required to move the load,
W = weight required to be lifted by the screw jack,
Alpha = angle of the screw helix,
Mu = coefficient of friction across the screw and the nut which is equal to tan phi (where phi is equal to the angle of friction)
**Efficiency of a Screw Jack - may be defined as the ratio between its input effort which is applied at the lever end to the magnitude of work done or the weight lifted by the screw jack device.
Analyzing the standard equation which is given as,
P = W tan (alpha + phi)
Where P = effort required to move the load,
W = weight required to be lifted by the screw jack,
Alpha = angle of the screw helix,
Mu = coefficient of friction across the screw and the nut which is equal to tan phi (where phi is equal to the angle of friction)
Now if assuming there would be no friction between the screw jack and the nut then phi would be equal to zero. The magnitude of effort P(0) requitred to lift the load would then be given by the expression,
P(0) = W tan alpha
Therefore efficiency = Ideal effort divided by actual effort = P(0) / P
Therefore efficiency nu = W tan alpha divided by W tan (alpha plus phi) = tan alpha / tan (alpha + phi)
The above final expression gives the efficiency of a screw jack and proves that it is not affected by the magnitude of load that’s being raised.