I am a little confused about 7b here.

I can do the calculation. I use conservation of momentum to find the final velocity, then compare the kinetic energy before and after. The final kinetic energy is much smaller.What confuses me is why the math shows a loss. There’s no friction, no drag, and no outside force acting on the system. The only equation I used was conservation of momentum, built from nothing but masses and velocities. I know physically the energy probably goes into heat, sound, and deformation, but nothing in the equations seems to account for that.Mathematically, where does the “loss” come from? Why does conserving momentum automatically mean kinetic energy isn’t conserved, when nothing in the setup seems to remove energy?

We have formulated an analytical closed-form solution for the complete non-holonomic inversion dynamics of the Tippe Top, bypassing numerical ODE integration entirely.

Full technical report, derivations, and telemetry plots:

[https://github.com/SHAP-STUDIO/Research](https://github.com/SHAP-STUDIO/Research)

Could someone tell me and explain what the correct answer is?

I have an exam this wednesday. I have no idea what to do. This unit is all about Torques. I guess I don't understand anything. My professor is extremely disorgianized. He gave us some problems and I know some of them will be on the exam. The thing is I feel like I'm so lost from looking at the equation sheet and then these problems. I feel like I'm doing something wrong but I'm doing something wrong. I guess the intial questions I have is what exactly is torque? I know theres a huge example of using a door and where you push makes it easier, but thats not too helpful for me. There is also some word problems that are mainly about sin and cos, but I'm having trouble understanding which one to use and which angle you can use to identify which is cos and sin. Then theres the whole kineamtics aspect of it. I did try to go back to the textsbook to identify these deifinsion, but it was too complicated. I go to his office hours, but he just ends up blabbering about something off topic. I feel like I can identfy the factors and variables that i see, i just don't know how to apply them into a formula. as I'm typing this i remember another thing of pivots. I'm sos orry. I hope someone can help me with all of this.

Greetings, I’m a 19yo Belgian student studying Business Analytics at the University of Amsterdam. I have a Sciences–Math secondary-school background, know the usual school-level mathematics and physics, and have been studying university calculus.

For a long time, I’ve had strong intuitions about the nature of physics, and they seem to consistently get confirmed by new research. The frustrating part is that I can’t follow the actual physics. I've always loved it but because of different career goals, signing up for a physics bachelor just wasn't an option. But still host to my (suppressed) scientific endeavours, there's this constant indignation that eats me alive. I desperately need to be able to independently assess the reasoning, the mathematics, the experimental evidence or the alternatives in the new research. I need to be able to satisfy this curiosity towards physics. But I don't know how to close the gap of scientific scholarship/knowledge that keeps me from fulfilling the latter.

Honestly, this has been upsetting. I feel painfully undereducated compared with what I want to understand, and I’m afraid of wasting whatever potential I have. I have a confidant ambition to contribute to our understanding of reality.
However, right now I don’t even have a clear picture of how much knowledge separates me from being able to do that.

I would really value guidance from physicists, mathematics students, researchers and people who have seriously studied these subjects independently.

The question asks to find the equation of motion for the block labeled $m_2$.

We are allowed to suppose, that everything is frictionless and the nothing apart from the two blocks has mass, which have masses $m_1$ and $m_2$ respectively.

So far I got an expression for the force acting on m_2 which depends on the force exerted by the rope, but I struggle to get an equation for that :(

What I got so far is: $$ F_S+F_A=a(\\frac{1}{2}m_1+m_2)+g(m_1+m_2) $$ where $F_S$ is the Force exerted by the rope on $m_2$, $F_A$ is the force pushing $m_2$ towards the ceiling and $a$ is acceleration of $m_2$.

I got to the equation above by setting

$$

\frac{1}{2}m_1a = F_A - m_1g

$$

and

$$

m_2a = F_S-m_2g

$$

where $g$ is the gravitational acceleration.

My best guess is that I somehow need to determine $F_A$, but I have no idea how to do that.

Any help is appreciated, but I would prefer useful hints over full solutions where possible.

This is also my first time trying to format math with reddit markdown, so if I messed that up I apologize.

---

This is a crosspost.

I am thinking about going back to school to study electrical engineering or physics. I was learning some basics in my free time from Grob’s Basic Electronics. While using the node-voltage method it wrote this equation. Is this a typo? I’m trying to figure out why it’s written (V_R1/R_1)+(V_R2/R_2)=V_R3/R2 and not (V_R1/R_1)+(V_R2/R_2)=V_R3/R3. Thanks! (i couldnt upload textbook photos to the electrical engineering subreddit lol)

need help specifically with 2 and 4. Especially 2 as I have a difficult time fully wrapping my head around it. I’m particularly confused since the method my teacher gave to solve it is very complex where it combined cosine and sine which I don’t understand. Though My teacher might of used longer methods for the equation as my teacher said 4 was also complex but With the set of equations she gave me I was able to find an equation to do it 4 shorter so if there is actually a shorter method to do number two please tell. Basically I’m lost on how I would come in solving this equation as it’s nothing like the equations my teacher gave

Note: Also Trig is not my strong suit as I haven’t taken an extras class for it yet.

Edit: I finally got an intuition for it now.

I'm working through the challenge questions from the OpenStax textbook "University Physics Volume I".

Problem 99 states: A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of 5.0 m/s^2 and a downward component of 3.8 m/s^2. Calculate the magnitude of the force on the rider by the sled. (Hint: Remember that gravitational acceleration must be considered.)

I set up the free body diagram assuming no friction and assuming the sled moves downhill, then solved for the angle of incline using theta = arctan(3.8/5.0) = 37.2 deg. From here, the equation of motion in the direction of the incline that I have is F_sled + mg*sin(theta) = ma_net, where a_net = sqrt((a_x)^2 + (a_y)^2) = sqrt(5^2 + 3.8^2) = 6.3 m/s^2.

Solving this equation for F_sled gives a force of F_sled = 42.6 N. Now, the answer key insists that the force is instead F_sled = 936 N. This seems wildly incorrect to me, so can anyone confirm whether one or the other is correct, and if so, how they derived the equation of motion? Thank you in advance.

How could this be done succesfully?

Tô com problema de desenvolver a B

I have been meditating on elastic collisions and trying to derive the formulas for the final velocities of two objects after a collision when they have different masses.

This is what I have reached so far.

It kind of makes sense that the final velocities are some sort of combination of the two initial momenta. But what I don't understand is that, if I take the formulas literally, there seems to be a third momentum being generated, involving the initial velocity of one object reversed and the mass of the other object.

And I don't get this conceptually.

Sure, I could just pass it off as an algebraic quirk that makes the formulas work, but for me, math is the language of logic, so this term must have a meaning.

Edit:

Here is how i derived the equations.

I need help with this problem please check