The servo has a maximum torque = 3lb-in.
The weight of the slider to be lifted to at least a height of 2-inches is = 1.00 lb
Therefore the distance at which the servo should be away from the slider is calculated using moment equilibrium.
Let x be the distance at which the servo is theoretically supposed to be placed away from the sliding collar.
Then;
3lb-in = 1lb × x
Therefore x = 3 inches
Power = torque × angular rotation
Since the crane is expected to lift the weight twice in 30 seconds.
The time to lift it up 2inches high is 30 ÷ 4 = 7.5 seconds
Therefore the power is = (1 lb × 3in) / 7.5sec = 0.4 lb-in/sec
Power ÷torque = angular rotation
0.4 lb-in/sec ÷ 3lb-in = (2/15) rad/sec = 7.64 ˚
Using law of Sines we get a theoretical height of 4.67 inches.
Therefore the fraction of the torque that it uses theoretically to lift 2 inches is 0.428.