Mechanics deals with motion and the forces that produce motion.

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In order to increase mechanical advantage, this ratio must increase which means making the effort distance longer and this can be accomplished by lengthening the length of the ramp.

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_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{70 lbs. \times 1 ft.}{65 lbs.} \) = \( \frac{70 ft⋅lb}{65 lbs.} \) = 1.08 ft.

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.

Tension is a force that stretches or elongates something. When a cable or rope is used to pull an object, for example, it stretches internally as it accepts the weight that it's moving. Although tension is often treated as applying equally to all parts of a material, it's greater at the places where the material is under the most stress.