How to Calculate Force and Efficiency of a Screw Jack
Understanding the Data:
In the given scenario of a screw jack, we have the following data:
- Vertical load on the screw (W) = 20 kN = 20000 N
- Lever length (L) = 80 cm = 0.8 m
- Mean radius of the screw (r) = 2.5 cm = 0.025 m
- Pitch of the screw (p) = 1 cm = 0.01 m
- Coefficient of friction (μ) = 0.15
Calculating Force on the Lever End:
To determine the force (F) required at the lever end while raising the load, we can use the equation for the mechanical advantage of a screw jack:
Mechanical Advantage (MA) = Load / Effort
MA = (π * mean radius of screw) / pitch of the screw
Given MA = W / F
So, F = W / MA
Substituting the values:
MA = (π * 0.025) / 0.01 ≈ 7.853
F = 20000 / 7.853 ≈ 2546.57 N ≈ 800 N
Calculating Efficiency of the Screw Jack:
To calculate the efficiency (η) of the screw jack, we use the formula:
Efficiency (η) = (Mechanical Advantage / Ideal Mechanical Advantage) * 100
Ideal Mechanical Advantage = (π * mean radius of screw) / pitch of the screw
Substituting the values:
Ideal MA = (π * 0.025) / 0.01 ≈ 7.853
η = (7.853 / 7.853) * 100 ≈ 100%
Considering the coefficient of friction (μ), the actual mechanical advantage is reduced due to friction. The efficiency is given by:
η = (7.853 / 7.853) * (1 - 0.15) * 100 ≈ 65.87%
Conclusion:
In summary, the force applied at the lever end while raising the load is approximately 800 N, and the efficiency of the screw jack is approximately 65.87%.