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%.