Questions relating to Newton's Laws of Motion

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1answer
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Calculate velocity $\nu$. [on hold]

A lorry of mass $3.5\times10^4\text{ kg}$ attains a steady speed $\nu$ while climbing an incline of $1$ in $10$ with its engine operating at $175$ kW. Find $\nu$. $g=10ms^{-1}$. Neglect friction. The ...
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1answer
24 views

Kinematics Mechanics Find the length of the belt and the speed of the rack. [on hold]

For A. I know that the formula for belt is simply $L=\frac{Pi(D_a+D_b)}{2}+2C+\frac{(D_b-D_a)^2}{4C}$ Which gives me $L= 116.99"$ since C is equal to $50$ For B. However I'm stuck and can't get the ...
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1answer
22 views

Understanding elastic collision between two rocks with unknown masses

I have this problem here that goes like this: Two curling rocks of equal mass, one red and the other yellow, are involved in a perfectly elastic, glancing collision. The yellow rock is initially at ...
0
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1answer
27 views

Comparison of Cartesian and Scalar Notation in Mechanics

In his book on Engineering Mechanics - Statics, R C Hibbeler provides many force problem solutions in both scalar and Cartesian notation (e.g Example 2.5 Chapter 2). It feels like he is trying to ...
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1answer
36 views

Two blocks and a frictionless pulley problem

Block B ($m_{B}$=0.36 kg) is connected to a lightweight rope that passes over a lightweight, low-friction pulley.The other end of the rope is connected to Block A ($m_{A}$=0.72 kg), which is on a low-...
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0answers
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Question about G-Forces and Circular Motion on a Human Centrifuge

I don't really understand what a G-force is and how it can be used to solve problems using the formula: $$T=mv^2/r$$ T is tension, m is mass (in kg), v is velocity (m/s) and r is radius of the circle....
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1answer
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The radius of the track.

A racing car completes $5$ rounds of circle in $2$ mins . It has uniform centripetal acceleration $\pi^2 t^{-2}$ then the radius of circle is?. I asked it on physics $SE$ but I dont know how to ask ...
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1answer
27 views

Accelerate to Max velocity, then decelerate to known velocity

I have an object traveling at a known velocity (Vi). It then accelerates (known A) to a known maximum velocity (Vmax), then decelerates (-A) to another known velocity (Vf). The total distance ...
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0answers
8 views

Function to represent discrete forces

I am trying to describe the force exerted by the two wheels of a 2d model of a car (one wheel in front of another) each with a magnitude of $F$. Is there any function I could use besides a piecewise ...
1
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1answer
24 views

Poisson brackets of angular momentum

So I'm trying to simplify this Poisson bracket of angular momentum vectors: {$L_1,L_2$} Where $L=r \times p$ I know that $L_1=r_2p_3-r_3p_2$ and $L_2=r_3p_1-r_1p_3$ (I can easily derive this from ...
3
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1answer
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Mathematical prediction of synchronizing multiple cams.

I am not a mathematician so be gentle with me but what kind of math equations (or what field of mathematics) would be needed for the following: I have designs for an old-style mechanical device I am ...
1
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1answer
45 views

Simple rocket model

I have a problem creating a model for a horizontal rocket flight. I want to model a rocket with constant force, drag constant and gravity. I also have to account for a changing mass and drag. I know ...
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0answers
7 views

Mixed convection - Matlab

So I am trying to solve the following mixed convection problem in Matlab: for $x=0: u=v=0, T=Th$ (heated wall); for $x=L: u=v=0, \frac{\partial T}{\partial x}=0$; for $y=0: u=v=0, \frac{partial T}{\...
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2answers
24 views

The position of a point mass that moves in a straight line .. / Determine the units

The position of a point mass that moves in a straight line is given by $x(t) = At^2 + Bt + C$, where $t$ is time. Determine the units of $A$, $B$ and $C$. The answer to the question is [A] = M/S^...
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0answers
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Elastic Body Simple Deformation

In continuum mechanics we can consider a reference frame $B = [0,1]$ along with a homogeneous deformation $F$ where $x = Fp$ for $x \in \mathbb{R}$ and $p \in [0,1]$ and $F = 2$ so $F[B] = [0,2]$. ...
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0answers
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Bead on rotating hoop with mass, determine the lagrangian

"Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop free to rotate about ...
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5answers
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Why don't we differentiate velocity wrt position in the Lagrangian?

In Analytic Mechanics, the Lagrangian is taken to be a function of $x$ and $\dot{x}$, where $x$ stands for position and is a function of time and $\dot{x}$ is its derivative wrt time. To set my ...
4
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1answer
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A criterion for area preserving dynamical system

In my investigation of dynamical systems I was met with this seemingly easy question I could not find an answer to: If we have a two dimensional system of autonomous ODEs viewed as a 2D dynamical ...
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2answers
33 views

Difficult projectiles question

A particle $P$ of mass $m$ lies on a plane inclined at an angle $\alpha$ to the direction vector $\mathbf{i}$. At $t=0$ the particle is projected from the origin of the coordinate system with speed $U$...
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0answers
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Taking Moments About a Point

This is a rod attached to a wall by a light inextensible string: And here is a diagram showing the forces acting: I want to find the normal reaction $R$ between the rod and wall using moments ...
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3answers
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I did a Maths question on mechanics using calculus and physics students disagreed, why are the solutions different? [duplicate]

So, I did the following question and got 2 different answers. Question: A lighthouse located 300 metres from a straight shoreline sweeps its beam of light around in a circle at a constant rate of 1 ...
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0answers
34 views

About periodic trajectories of a Hamiltonian system

Consider a Hamiltonian system with Hamiltoniana $H (\mathbf{q}, \mathbf{p})$, where $H$ doesn't depend on time $t$. It is known that in some domain of phase space the trajectory of system are peiodic. ...
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2answers
34 views

Compute the following line integral along a path of your choice (Finding potential)

Consider the following vector field: $$\vec A(x,y,z)=(yz)\hat i+(xz)\hat j+(xy)\hat k$$ Compute the line integral of $A$ along a path of your choice connecting $(0,0,0)$ to $(1,1,1).$ I recognise ...
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2answers
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Second order non linear differential equation: Central force question

The problem is as below: I have derived that the particle satisfies the motion equation $$ \frac{d^2u}{d \theta ^2 } + u = \frac{F(1/u)}{mh^2u^2} $$ by Newton's Law, $u= 1/r$ and $h = r^2 \frac{d \...
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1answer
39 views

Stream function and Vorticity relationship with Streamlines

For a two-dimensional flow, the velocity is given by $\textbf u= (u(x,y,t),v(x,y,t),0)$. Define the stream function $ψ (x,y,t)$. Evaluate $(\textbf u·∇) ψ$ and deduce a relationship between the stream ...
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0answers
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Time-$t$ map of a Hamiltonian flow: how to check twist property?

I would like to obtain a general formula to verify if a certain time-$t$ map of a Hamiltonian flow is twist. I have a Hamiltonian $1$ degree of freedom system $H=H(q(t),p(t))$, such that all orbits ...
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0answers
11 views

How to model a point force with uncertain concentration point?

I consider a beam which is bent under influence of a point force concentrated at some point $\xi$ of the beam. The exact co-ordinate of $\xi$ is not known, but it is known a neighbourhood $(l_0,l_1)\...
0
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1answer
23 views

Conservation of Net Mechanical Energy in SHM

I have a question I wish to answer: Show that the simple harmonic motion solution of the simple pendulum in the form $$\theta (t) = A\cos ({\omega _0}t)$$ (constant A) conserves net mechanical energy ...
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0answers
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A soft question on Gauge Equivalence in Integrable Systems

I have a question about two well-known spectral problems in Integrable Systems. These are the Dirac and the ZS-AKNS spectral problems. They are are known to be gauge equivalent (please see equations (...
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0answers
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Calculate Universal Time for when an object in orbit reaches a given radius / altitude?

Assuming that an object in orbit WILL reach a given radius / altitude at some point in the future, how can I work out the exact time it will reach that point? Assume that the object is a Satellite in ...
2
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1answer
25 views

Gravitational Potential Energy Near the Surface of the Earth…

Okay so for an object of mass m at a distance r from the Earth's centre, the GPE is $$U(r) = {{ - GMm} \over r}$$ For an object at height z above the surface (which obviously means at radius $r = {r_{...
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1answer
46 views

Finding pressure using Bernoulli's Theorem

The inviscid irrotational flow around a circular cylinder of radius $a$ is described by the complex potential $$w =Uz+ \frac{Ua^2}{z}$$ where $U$ is a positive constant. I found $\psi=U \cos \theta (...
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1answer
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Why is $\omega $ the natural/angular frequency?

Pardon me cause I'm a little confused. If we have something like: $y=A\sin \left( \omega t-\delta \right)$ why would $\omega$ be considered the natural frequency? I always thought the frequency of a ...
1
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1answer
64 views

Finding stagnation points and stream function

Sorry for the lack of latex. The question I want to ask would need all this info and it would take very long to write it. (a) Irrotational flow means $\nabla \times \textbf u =0$ so we can define ...
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1answer
22 views

Viscous fluid boundary condition

Consider an incompressible viscous fluid of kinematic viscosity $ν$ , dynamic viscosity $µ$ and density $ρ$ . A viscous boundary layer is located over a solid surface at $y = 0$ and $x > 0$. The flow ...
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1answer
79 views

Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
1
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1answer
24 views

Manipulating vorticity equation

We have $\omega = (0,0, \xi(x,y,t))$ and $\textbf u =(u(x,y,t),v(x,y,t),0)$ and that $$\frac{\partial \xi}{\partial t} +u \frac{\partial \xi}{\partial x} +v\frac{\partial \xi}{\partial y}=0$$ is a ...
2
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1answer
48 views

Finding pdes of velocity component and pressure

An incompressible viscous fluid of constant density $ρ$ and kinematic viscosity $ν$ occupies the space above a solid boundary at $y = 0$ in two-dimensional Cartesian coordinates $(x,y)$. For time $t &...
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1answer
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Finding an expression for velocity [closed]

Consider an annulus formed by two circular cylinders, with one cylinder inside the other. The inner cylinder has radius $a$ and the outer cylinder has radius $b$. The cylinders have a common axis, and ...
1
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1answer
84 views

Figuring out velocity,acceleration, work of a particle given that we know its position vector.

Recently this question came up in a problem class of mine. A particle moves in such a way that its position vector at any time $t$ is $\vec{r}(t)=\pmatrix{A\sin{\omega t}\\A\cos{\omega t}\\Bt^2}$, ...
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2answers
26 views

Resolving Forces in an inclined plane ( Mechanics )

I have exams after a few days and I'm doing all I can to understand the concept of resolving forces. With hard luck and a few hours of devotion, I acquired basic knowledge on Resolving Forces and was ...
0
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1answer
28 views

Understanding shift to polar coordinates in the newtonian central force system of ODE's

This is from Hirsch, Smale and Devaney chapter 13. The larger context is moving towards blowing up the singularity at the origin of the system. The second order ODE is defined, $X:t\rightarrow \...
0
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1answer
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What direction would a hinge's reaction force point?

In my homework question there is a ladder with the bottom touching the smooth floor and the other end is attached to a hinge. I need to draw a force diagram and use that to find the normal. There is ...
0
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1answer
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Object of unknown mass in simple harmonic motion… [closed]

An object with mass m in simple harmonic motion on a vertical spring is observed for 5 full oscillations. The time is measured to be 13 seconds. What is the angular frequency (3dp)? A previous ...
0
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1answer
22 views

A question about a pendulum moving in simple harmonic motion

For a 2.7kg mass oscillating in simple harmonic motion (spring constant: 360N/m) with an amplitude of oscillations measured at 3.4cm. How do I calculate the total mechanical energy, maximum speed and ...
0
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1answer
16 views

Integrating equation with square on the bottom.

Say you are working with acceleration as a function of displacement and you are using calculus. $a = \frac{1}{(s - 600)^2}$. If you wanted to obtain velocity you'd use $a = v\frac{dv}{ds}$ so $vdv = ...
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0answers
6 views

Angular velocity using Euler's dynamical equation

using Euler's dynamical equation for force free motion of a rigid body,symmetrical about Z-principal axis,with angular velocity $W=(w_1,w_2,w_3)$ where $I=1,2,3$ are the components along the three ...
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1answer
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Motion of a pendulum equation in the George Simmons book on differential equations [closed]

I just can't understand the transition between this two formulas, why $dt$ becomes $T/4$. Can anybody help me with that?enter image description here
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0answers
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Sketch the phase portrait

I'm asked to sketch the phase portrait for the potential given below. Also below is my attempt of sketching the phase portrait. I appreciate that my sketch is not fantastic but is it correct? phase ...
3
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2answers
32 views

What does it mean to use levi civita symbol with Poisson brackets in this way

I'm doing some studies in mathematical methods for physics and I came across something that I don't really understand. I have only been using the $\epsilon_{ijk}$ when I cross some vectors or ...