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13

The confusion comes from how you have written the equation. If you write it like this $$F_{net} = ma$$ it will be easier to see your error. You are exerting a force on the boulder, but net force is zero. This means that other forces such as friction are canceling your force out. In this case. Friction equals applied force.


8

Since the Lagrangian results in exactly the same equations of motion as Newton's laws, I'd say that based on their agreement with experiment both are on equal footing. Of course, to get the right equations of motion from Lagrange's equation you have to pick the right Lagrangian, so then you ask how we systematically pick the right Lagrangian. The recipe in ...


4

No. The easiest way to see this without invoking rotating reference frames is to write out Newton's Law's in polar coordinates, which work out to be: \begin{align*} F_r &= m \ddot{r} - m r \dot{\phi}^2 \\ F_\phi &= m r \ddot{\phi} + 2 m \dot{r} \dot{\phi} \end{align*} From these, it's pretty easy to see that if we have $F_\phi = 0$ and $\dot{r} ...


3

Your profile lists your age as 17, so I assume you're still at school. At this stage in your physics education you'll only have been exposed to differential equations that have relatively straightforward solutions. I assume the education system does this to avoid putting you off. If you continue studying physics you'll quickly learn that the vast majority of ...


1

Your question is very confusing, so I will first attempt to answer the spirit of your question with a cleaner scenario. It is possible to "move" from one place to another if there is minimal friction. You can do so with yourself, a large box, and a bag full of baseballs. But it isn't as cool as it sounds (that is why I had to put quotes around move). If ...


1

The rule is simple: regardless of which forces are acting, if the motion is accelerated then there is a net force, otherwise, there not net force. The only kind of non-accelerated motion is motion in a straight line at uniform speed. In particular you options: a)wrong, at it is accelerated in the curved part. We do not know in the straight part. b)wrong, ...


1

The answer to this question is very much analogous to the answer to how aeroplanes fly. See Physics SE Question "What Really Allows Airplanes to Fly?" and the best (IMO) answer is this one here. But basically the airfoils, sails or vanes - whatever they may be called - deflect the flow of air. They do this by pushing on the air and changing the latter's ...


1

You're correct that (B) is incorrect, but for the wrong reason. Kinetic energy doesn't have to be conserved since, in any closed system with only conservative forces, mechanical energy is conserved. There are many physical situations where kinetic energy isn't conserved (inelastic collisions for example), hence we do not know kinetic energy is conserved. ...


1

With a strong grasp of Lie Algebra and Calculus of variations, "Invariante Variationsprobleme" should provide all the foundation one needs to build Newtonian Mechanics (and so much more). The deeper reason that we use either of these formalism is that they agree with experiment; that either formalism predicts the other is far less valuable than that they ...


1

The main thing is that the total force you are applying on the body is not enough to move the rock.This means that the total force on the box is zero because the force of static friction is grater than that of your applied force,which cancels out the effect your force.As your forces increases the static friction also increases until a point comes when you ...


1

For a particle in a gravitational field treated as a constant? Surely Newton's equations of motion in the fixed rectangular frame: $$\ddot{x}=0$$ $$\ddot{y}=-g$$ are as simple as it can get!



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