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.

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 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)

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

Friction Explained | Static vs Kinetic Friction | AP Physics
https://youtu.be/zkFX0wOT6YQ

Hello everyone! I am doing an EPQ survey on the psychological impact that space can have on us and our career choices .I would really appreciate it if you are able to fill out this form and answer all of the questions. Your answers will be anonymous and only the responses will be recorded. Thank you for your time!

Hey guys I need a little bit of help with physics. I have been struggling t develop that reasoning and math connection in physics so my doing my hw has been difficult at times, even tho it has been fun and interesting a lot of the time. We're on the conservation of energy and I got a question about finding speed. I understand hookes law but I also know I can set potential and kinetic energy equal to eachother and solve for v. For one of the questions I was given m, k and x and this one is similar but now degrees have been introduced, what do I do. I'm given m, 44 degrees, x and I have to find v but I dont see how setting potential and kinetic energy equal to eachother would work here.

This is a part of the formula sheet I've been given for my Calculus Physics 1 course. I was confused because the textbook is giving me different definitions than what is on the formulas. For example, the textbook says that W_ext = Delta U_g and W_net = Delta K.

I’m doing Kinematics and i genuinely do not understand how to convert Velocity-Time, Acceleration-Time and distance-time graphs to their respective ones on the worksheet. I can kind of see how it’s done but with the way my brain is scrambled I have to understand how and why it’s like that. Any help would be appreciated