Answer to Question #168854 in Mechanics | Relativity for April

Question

The pitch of a jackscrew shown in figure 2 is 0.3 cm and has a lever arm of 60 cm length. What

force at the end of the lever arm will raise a load of 190 kg if the efficiency of the machine is

12 %?

Answer 1

The force, required to raise a load of mass m is:

$F=\frac{mg}{AMA},$

where AMA - actual mechanical advantage.

$AMA=E\frac{d_2}{d_1},$

where E - the efficiency of the machine;

d₁ - the pitch of a jackscrew;

d₂ - the distance, that the input force moves to raise a load on the distance d_1.

Distance d₂ is equal to the lenght of complete circle with the radius r, that is equal to the lenght of the lever arm.

So,

$F=\frac{mgd_1}{E\cdot 2\pi r}=\frac{190\cdot 9.8\cdot 0.003}{0.12\cdot 2\cdot 3.14\cdot 0.6}=$ 12.3 N.

Answer: 12.3 N.