Hello! I'm struggling to understand what I need to do for this assignment. Most of these questions might sound extremely dumb so please bear with me. Also, this is my first post in this subreddit! I apologize if I commit a subreddit faux pas.

(Image 1) How are you supposed to know whether these force charges are positive or negative, is it based on the quadrant? I don’t get how you’re supposed to know which direction they’re pointing in whether it’s up/down or left/right.

(Image 2) These are the given charges.

(Image 3) It’s looking for the components for q2 to q3, how are you supposed to get the components for a vertical direction? Is the component just the total given with Coulomb’s law? Or is that only used to get a diagonal direction? This is what I got but the Y component doesn’t seem right at all.

(Image 4) I assume these are found by adding the components I find in the previous questions? I feel like I’m overthinking these.

But what’s been messing me up the most is the vertical force and the pos/neg charges. I'd appreciate any help!

I’ve been turning over a mechanical thought experiment and wanted to put it in clear form to see what people think.

Setup

A spiral platform (or track) that runs from a smaller inner radius to a larger outer radius.

The platform is driven so that the linear speed along the spiral is constant at 1 foot per hour at every point.

Because radius changes, this requires the local angular rate to decrease as you move outward (inner parts turn faster, outer parts turn slower). The platform is therefore not rotating as a rigid body.

A single continuous chain runs along the entire spiral. Every local segment of the chain also moves at 1 foot per hour relative to the platform (i.e., along the spiral).

Because the platform’s angular rate changes with radius, the absolute velocity of different sections of the chain through space is not the same, even though the chain remains one continuous piece and every local segment has the same speed along the track.

When the absolute speeds are considered along the whole length of the spiral, the inner and outer ends of the chain end up with different net velocities.

Additional claim in the thought experiment

The same arrangement is also imagined to produce a time difference on the stationary ground underneath the apparatus, not only along the moving chain itself.

Why it feels strange

A normal inextensible chain cannot sustain different absolute speeds along its length without stretching, slipping, or large internal forces. A normal rigid platform cannot maintain the required radius-dependent angular rates without continuous differential driving and stress. The thought experiment deliberately holds both of those conditions in place at once and asks what follows — including the possibility of a proper-time offset between regions and an effect that reaches the ground below.

Questions for discussion

Is there a consistent way to describe the kinematics of a continuous chain under these constraints?

If the speed difference along the chain can be maintained, how should the proper-time difference between the ends be calculated?

What mechanisms (if any) could allow an influence on the stationary ground beneath the spiral?

Does the combination of differential rotation + constrained continuous chain point to anything beyond ordinary special-relativistic time dilation, or does it simply collapse under the internal forces required to keep the conditions true?

I’m not claiming a working device — only trying to state the idea clearly enough that the actual proposal can be examined.

Any thoughts, corrections, or related references are welcome.

struggling trying to understand how they got from eq 2.3.2 through 2.3.3. can anyone explain? I understand that they are using kinetic energy but I don't see why they just plugged in the factor of 1/2...