Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where E_d is the effort distance and R_d is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{2 ft.}{0.5 ft.} \) = 4

You might be wondering how having an effort distance of 4 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 4 times the resistance distance, the effort force must be \( \frac{1}{4} \) the resistance force. You're trading moving 4 times the distance for only having to use \( \frac{1}{4} \) the force.

Collinear forces act along the same line of action, concurrent forces pass through a common point and coplanar forces act in a common plane.

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE linearly while an increase in speed increases KE exponentially.

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 = \( \frac{R_bd_b}{R_a} \) = \( \frac{70 lbs. \times 7 ft.}{60 lbs.} \) = \( \frac{490 ft⋅lb}{60 lbs.} \) = 8.17 ft.

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 5 ft. = 370 lbs. x 3 ft.
F_e = \( \frac{1110 ft⋅lb}{5 ft.} \) = 222 lbs.