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On the atomic or molecular scale, why gravitational forces play no role because electric forces are enormously stronger?

Assume that you weigh 500 N. If you are falling down through the air at constant speed, the force of the air against your body is
a) zero
b) more than 0 but less than 500 N
c) 500 N
d) more than 500 N
e) need more information
Explain with thorough reasoning.

Describe the gravitational forces.

In the equation $\stackrel{\to <!--\; \to \; -->}{F}=m\stackrel{\to <!--\; \to \; -->}{a}$ is the acceleration vector always in the direction of the force vector, I mean why can’t they be in the opposite direction? Will this relationship break down in some scenario?

If one defines force as the time derivative of momentum, i.e. by
$\stackrel{\to <!--\; \to \; -->}{F}=\frac{d}{dt}\stackrel{\to <!--\; \to \; -->}{p}$
how can this include static forces? Is there a generally accepted way to argue in detail how to get from this to the static case? If not, what different solutions are discussed?

A force F directed upwards is applied on an object resting on a flat surface. The object then moved to the right. Which of the following is TRUE about the upward force?a. F does work on the objectb. F is a conservative force c. F is gravitational forced. F caused the displacement of the objecte. Only the 1st and 3rd optionsf. Only the 2nd and 4th optionsg. None of the above

From classical mechanics, the force on a spring is given by the negative gradient of the potential energy with respect to position or displacement.
Can we also say $F=-<!--\; -\; -->\mathrm{\partial <!--\; \partial \; -->}U/\mathrm{\partial <!--\; \partial \; -->}x$, where U is the "internal" energy of the spring?

Can the second law of motion for rotation, $\stackrel{\to <!--\; \to \; -->}{\mathrm{\tau <!--\; \tau \; -->}}=I\stackrel{\to <!--\; \to \; -->}{\mathrm{\alpha <!--\; \alpha \; -->}}$, be used for any axis?
Is there any case that acceleration $\stackrel{\to <!--\; \to \; -->}{\mathrm{\alpha <!--\; \alpha \; -->}}$ is not in the direction of applied torque $\stackrel{\to <!--\; \to \; -->}{\mathrm{\tau <!--\; \tau \; -->}}$?

The total energy of an object comes from the time part of the four-momentum, and so isn't a Lorentz invariant. On the other hand, is the potential energy of a compressed spring a Lorentz invariant?

In my lecture today my professor briefly mentioned that force is the derivative of energy but I did not really get what he meant by that. I tried to express it mathematically:
$\frac{d}{dt}{K}_E=\frac{d}{dt}\left(\frac{1}{2}m{v}^2\right)=mv\frac{dv}{dt}$
This looks really close to Newton's second law $F=ma$ but there is an extra "v" in there. Am I missing something here?

When an astronaut with a mass of 55 Kg goes from Earth to the Moon, how much does their weight change? Answer in N OR in Pounds. gmoon= 1.62$=9.8m/s^2$, gearth$=9.8m/s^2$

While working with problems on elastic collisions, I have come across this observation, that the elastic potential energy of a two-body system is the maximum when the relative velocity equals zero. In fact, the same applies when we are talking about a 2-block+spring system. Why is it so?

We choose a system to be a spring + a connected body. If we stretch the body and leave it, it will make a simple harmonic motion. The center of mass of this system is approximately the center of mass of the body because the spring has a negligible mass. Newton's second law states that: $F_{external}=M{a}_{cm}$ However, it is apparent that the center of mass has an acceleration though the total external force on the system is zero. What is the explanation?

Non-Constant Acceleration due to Gravity
Recently, I had the first physics lab for my university physics course. This lab was fairly simple, as we were merely using a computer and a distance sensor to graph the position, velocity, and acceleration of a cart as it moved along a linear track.
One of the situations we captured data for involved starting the cart at the bottom of an inclined ramp and giving it a push upwards. As expected, it rolled up, came to a stop, and then came back down the track to its starting position. The position-vs-time graph was essentially parabolic, the velocity-vs-time graph was essentially linear, and the acceleration-vs-time graph was essentially linear. So far, so good.
At this point in the lab, the instructor pointed out that, if the data was examined closely, the acceleration of the cart was greater while the cart was traveling upwards than when the cart was traveling downwards (approximately $0.546\frac{m}{s^2}$ and $0.486\frac{m}{s^2}$, respectively), and asked us to determine why in our lab report.
Now, gravity was the only force acting upon the cart, and thus it's acceleration should be a constant, at least at the scale our experiment was conducted at, so these results are completely baffling my lab group. So far, we have proposed the following ideas, but none of them seem very plausible.
Doppler effect on the ultrasonic distance sensor
Friction
Air resistance
Human error
The first seems highly improbable, and the last three are more obfuscation and hand waving than actual theories.
Why does our experimental data show the acceleration due to gravity to change based on the direction the object is moving?

Meaning of acceleration due to gravity
I found article in which it is said that it would be incorrect to say that g is not acceleration due to gravity but local gravitational field as there is no acceleration on a block placed on a table. Please can you explain this as I am in a school and I have read only that g is acceleration due to gravity and textbooks say this too.

Acceleration due to gravity during its journey up and down
When we throw an object up into the air, ignoring air resistance, etc, we define acceleration to be -9.8 m/s^2. When it goes down after its journey up, like a parabola, do we define the acceleration as 9.8 m/S^2, OR still the same as -9.8m/s^2?
I know that acceleration due to gravity is always constant, but would it be wrong to say it like the question i have above?

The force that accelerates a rocket into outer space is exerted on a rocket by the exhaust gases. Which Newton’s Law of motion is illustrated in this situation?

How do you calculate the acceleration due to gravity of a massive object (black hole)
Is there an online calculator to find the acceleration of gravity a massive object exerts from a specific distance? I know the effects of gravity kind of just fade out with distance but I'm asking for mass-specifics.
For example, you plug in the mass of the object and the distance from the object to get the m/s^2 (and maybe even the escape velocity)???
(I'm also thinking this would be some sort of exponential graph, like "acceleration" on the y axis and "distance" on the x axis)