4. in the exploration, the sled does not move at all when two equal forces are applied
opposing directions. explain the reason behind this.

The net force is zero, so the acceleration is zero

Explanation:

Newton's second law states that the acceleration of an object is proportional to the net force applied to it, according to the equation:

(1)

where

is the net force on the object

m is the mass of the object

a is its acceleration

In this problem, we have a sled acted upon two forces, . So the net force on the sled is

(2)

however, we are told that the two forces are equal in magnitude but in opposite directions, so

So, eq.(2) becomes

and so eq.(1) becomes

which means

so the acceleration of the sled is zero, and if the sled was at rest, it will not move.

most voltage drop calculators want the distance between the source and destination. then internally, they double it so both the source and return wires are calculated. but you need to know which distance the calculator uses so you're not half of what you should be or double what you should be.

most circuit breakers will not take a #6 directly, so the electrician will have to splice on a smaller pigtail. you also have to upsize the grounding wire when you upsized the ungrounded (hot) wire (see note in 250.122). this will preclude using most cable assemblies, as a cable with #6 copper will most likely only have a #10 grounding conductor. you need a #6 grounding conductor if the circuit is 20a. a #8 cable is no better, as it will have a #10 grounding conductor too. but most 20a breakers will take a #8 directly.

in your related post, you didn't say what type of load this is. if it is a light or heater, voltage drop won't be a big issue. if this is a motor, the current needs are huge at startup and the voltage drop can pose a problem. if this is a motor, knowing if the motor is under much load during startup will answer the voltage drop effect (a saw is easier to start than a compressor).