For any given surface, the coefficient of static friction is higher than the coefficient of kinetic friction. More force is required to initally get an object moving than is required to keep it moving. Additionally, static friction only arises in response to an attempt to move an object (overcome the normal force between it and the surface).

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.

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

Solving for d_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{20 lbs. \times 3 ft.}{45 lbs.} \) = \( \frac{60 ft⋅lb}{45 lbs.} \) = 1.33 ft.

An inclined plane is a simple machine that reduces the force needed to raise an object to a certain height. Work equals force x distance and, by increasing the distance that the object travels, an inclined plane reduces the force necessary to raise it to a particular height. In this case, the mechanical advantage is to make the task easier. An example of an inclined plane is a ramp.

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 180 ft⋅lb and the resistance force is 60 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
180 ft⋅lb = 60 lbs. x d_resistance
d_resistance = \( \frac{180ft⋅lb}{60 lbs.} \) = 3 ft.