Question

A screw jack has a pitch of 1/2" and is turned with a bar 4' long. Calculate A) the MA, B) the load that can be lifted (theoretically) with a force of 50 lbs, C) the efficiency of the machine if a load of 10,000 lbs is lifted

Answer 1

A) the MA:

$\frac{F_{load}}{F_{in}} = \frac{2{\pi}r}{l} = \frac{2*\pi*4*12~\text{''}}{0.5~\text{''}} \approx 603.19. \\$

B)

$F_{load} = F{in}\frac{2{\pi}r}{l} = 50~\text{lbs}*\frac{2*\pi*4*12~\text{''}}{0.5~\text{''}} \approx 30159.29~\text{lbs}. \\$

C)

Mechanical efficiency measures influence of friction on the transformation of the input force into the effective load exerted on the force and is usually a dimensionless number between 0 and 1 (100%). Since no data on the friction or losses is included in the problem, one can only the efficiency is 1 (100% / ideal machine).