The mechanical advantage (MA) of a block and tackle pulley is equal to the number of times the effort force changes direction. An easy way to count how many times the effort force changes direction is to count the number of ropes that support the resistance which, in this problem, is 4. With a MA of 4, a 110 lbs. effort force could lift 110 lbs. x 4 = 440 lbs. resistance.

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.

The mechanical advantage (MA) of a wedge is its length divided by its thickness:

MA = \( \frac{l}{t} \) = \( \frac{25 in.}{5 in.} \) = 5

Newton's Law of Univeral Gravitation defines the general formula for the attraction of gravity between two objects:  \(\vec{F_{g}} = { Gm_{1}m_{2} \over r^2}\) . In the specific case of an object falling toward Earth, the acceleration due to gravity (g) is approximately 9.8 m/s². 

To balance this lever the torques at the green box and the blue arrow 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 = \( \frac{R_bd_b}{R_a} \) = \( \frac{50 lbs. \times 1 ft.}{65 lbs.} \) = \( \frac{50 ft⋅lb}{65 lbs.} \) = 0.77 ft.