The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 12 and the output radius (where the resistance is being applied) is 7 for a mechanical advantage of \( \frac{12}{7} \) = 1.71

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{25 lbs.}{1.71} \) = 14.62 lbs.

A concentrated load acts on a relatively small area of a structure, a static uniformly distributed load doesn't create specific stress points or vary with time, a dynamic load varies with time or affects a structure that experiences a high degree of movement, an impact load is sudden and for a relatively short duration and a non-uniformly distributed load creates different stresses at different locations on a structure.

Connected gears of different numbers of teeth are used together to change the rotational speed and torque of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

This problem describes an inclined plane and, for an inclined plane, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance:

F_ed_e = F_rd_r

Plugging in the variables from this problem yields:

F_e x 6 ft. = 340 lbs. x 1 ft.
F_e = \( \frac{340 ft⋅lb}{6 ft.} \) = 56.7 lbs.

Mechanical advantage is resistance force divided by effort force:

MA = \( \frac{F_r}{F_e} \) = \( \frac{150 lbs.}{50 lbs.} \) = 3