Questions relating to Newton's Laws of Motion

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2answers
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Determine the resultant force of the inclined plane

So I was given this problem for my statics subject. I'm just having problems getting the x and y components of the force $120$ lb. I know that $60$-lb Force $$F_x = (60\mbox{ lb})\cos20^\circ$$ ...
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0answers
18 views

Mechanics, Resultant of forces [on hold]

Two forces of magnitudes $xN$ and $yN$ act at a point $O$. The magnitude of their resultant is $zN$. Write down an inequality satisfied by $z$. The answer is $|x-y|\le z \le x+y$
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1answer
23 views

How to derive velocity out of acceleration in a circular motion?

A car starts moving in a circle with a radius of 200 meters. It has a constant tangential acceleration of $1{\text{m}\over {\text{sec}}^{2}}$. a. What is the angular acceleration? b. What is the ...
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0answers
25 views

Axioms of Newtonian Mechanics

Axiomatically speaking, could Newton's laws be derived (as theorems) from the conservation of momentum and energy -- along with a few suitable definitions of things like an inertia frame and force? ...
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0answers
23 views

Is there a difference between tipping and toppling [on hold]

In my mechanics modules I see toppling and tipping used where objects are at the point of falling over when pushed. Is there a difference between them? Can they be used interchangeably?
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0answers
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Questions about the mechanics of a spinning CD.

A CD is spinning counterclockwise with a radial velocity of $\omega=30\text{rad}/\sec$. The preface of what I did manage to solve and further details: I was asked what is the period time (12 seconds), ...
4
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2answers
171 views

How to Show Cotangent Bundles Are Not Compact Manifolds?

Hamiltonian mechanics occurs in a sympletic manifold called phase space. Lagrangian mechanics take place in the tangent bundle of the configuration manifold. Using Legendre transform makes possible ...
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0answers
14 views

Finding the range of a cannonball- proof verification.

I asked such a question before but I do learn best by mistakes and corrections.(I didn't fully understand it yet.) I could really use your verification: A cannonball is being fired with a velocity of ...
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1answer
18 views

How to get a range of a body being shot\thrown? Theoretical question.

I already asked a similar question here, but the answers were technical, leading me to no genuine comprehension of what I am doing.(I am not complaining or anything, I really thanked you then.) ...
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0answers
14 views

Evaluating vorticity as a function of velocity components.

So i have the following question.. Consider the axisymmetric flow of a viscous fluid u = ($ \frac{-\alpha r}{2} $, v(r), $\alpha z$) in cylindrical polar coordinates, where $\alpha$ is a positive ...
1
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1answer
12 views

Under what condition does $A^T(B \times C) + (B\times C)^T A = 2A^T(B \times C)$, A,B,C vectors

In my classical mechanics text book there is a formula that states $(\dot r_c + \omega_i \times d_i)^T (\dot r_c + \omega_i \times d_i)$ give rise to $\dot r_c^T \dot r_c + 2\dot r_c^T(\omega_i ...
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1answer
18 views

Lagrangian of bead on a rotating hoop

I'm trying to find the Lagrangian for a bead on a rotating circular loop (constant angular velocity $\omega$, radius $a$) in two different ways and I'm unsure why these are giving different answers. ...
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2answers
25 views

How to find the range of a cannon ball?

A cannon is positioned with a direction of 60 degrees between the ground and itself. (Sorry, again, for my poor English. I hope you understood that sentence.). The shooting velocity is ...
1
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3answers
55 views

Where have I gone wrong? A basic question in physics (Mechanics)

A stone is dropped vertically in a velocity of $15$ minutes per second, from a point $40$ meters above the ground (excuse my poor English.). a. How long will it take to the stone to hit the ground? ...
0
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1answer
19 views

Expression for $dW$ for a 3D position dependent force $\vec{F}(\vec{r})$.

I was looking at the derivation of the infinitesimal element of work done for a 3d position dependent force and I couldn't get over the switching of $\text{d}\vec{v}$ and $\text{d}\vec{r}$ in the ...
1
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1answer
48 views

Planetary Motion: A comet describe a parabola about the sun [closed]

A comet describe a parabola about the sun, show that the sum of the squares of the velocities at the extremities of a focal chord is constant. I have no idea how to solve. Please help. I only ...
1
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1answer
88 views

planetary motion: Particle describes an ellipse as a central orbit about a focus

A particle describes an ellipse as a central orbit about a focus. Show that the velocity at the end of the minor axis is the geometric mean between the greatest and least velocities. My attempt: ...
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0answers
38 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $? [migrated]

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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0answers
19 views

Equilibrium problem. (Mechanics).

Find the maximum weight that water bucket can take if each of the cables can carry a maximum of 10lb. I have worked as follows; $\sum F_y = 0$ $10sin(60)+10sin(180-tan^{-1}(4/3)) = W_{max} = ...
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1answer
17 views

Tracking an Object

I have the following situation, two objects A and B, at a distance of x from each other. Both objects have their own 2d heading Ah and Bh and their own speeds As and Bs. I'm trying to determine the ...
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0answers
21 views

Mechanics question Help

Two particles $A$ and $B$ both with masses $0.2kg$ move in the same direction with speeds $5ms$ and $3ms$ respectively. Both receive an impulse of $0.3ns$, show that the speed of $A$ after the ...
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1answer
17 views

Gyroscopic rotation.

I have never encountered a gyroscopic movement question so i am going to require some assistance. At the end of a rod of length $l$ is a solid disk with radius $R$, spinning with angular velocity ...
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0answers
31 views

Green's function in the context of classical mechanics

I am following this paper entitled "The classical mechanics of non-conservative systems". I would like to discuss equation (2) since I cannot get what the autor says. This is the problem: let's ...
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1answer
40 views

Derivative of an Infinitesimal?

I am currently studying calculus of variations (for my classical mechanics course). I have, on multiple occasions, seen the derivative of an infinitesimal quantity defined like below $$\frac{d}{dt} ...
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1answer
49 views

Inequality with Logarithms!

I need some help solving this inequality for a question involving the number of bounces, $n$, of ball such that the max. height of the ball is less than 5cm. This is the equation I have gathered from ...
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1answer
33 views

How to rearrange this equation and find the constant?

Okay so I've been working a mechanics problem and it has boiled down to this. I want to find $v(t)$ and I currently have that. $$t+c_1=\frac{1}{2\sqrt{gk}}\ln{\frac{\sqrt{g/k}-v}{\sqrt{g/k}+v}}$$ ...
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2answers
20 views

Mechanics limiting speed with variable radius.

Okay so I'm trying to solve this problem and have ran into some difficulties. Using impulse change of momentum principles I managed to figure out that the equation of motion for the hailstone is ...
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2answers
21 views

Question about dropping a ball and coefficient of restitution.

If I drop a ball from a height $h$ and the ball rebounds from the floor it will bounce back up to a height of $e^2h$ where $e$ is the coefficient of restitution between the floor and the ball. Why is ...
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0answers
14 views

Tension in the stretched string in equilibrium state

A smooth cylinder with circular cross-section of radius a is held with its axis horizontal. A light elastic band of unstretched length 2¼a and modulus of elasticity ¸ is wrapped round the ...
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1answer
10 views

Solving particle in vertical motion with air resistance using conservation of energy

A particle of unit mass is projected vertically upwards with speed u. At any height x, while the particle is moving upwards, it is found to experience a total force F, due to gravity and air ...
0
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1answer
13 views

Equation of motion and differential equations problem.

Hello I just worked through an old question I found online and was wanting some feedback on my answer (mainly if it was correct) or other improvements. Question Answer (a) $\frac{dF}{dt}=-k$ ...
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1answer
28 views

Classical mechanics Hamiltonian vector field.

On page 188 of Abraham and Marsden Foundations of classical mechanics, how "by construction" does \begin{equation} i_{X_{H}}dq^i=\frac{\partial H}{\partial p_i}\ \ \ \ \ \ \text{and} \ \ \ \ \ \ \ ...
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0answers
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Meaning of Torricelli's Equation ($v^2=u^2+2as$)

The equation of motion $v^2=u^2+2as$ is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) ...
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1answer
31 views

Show the Euler Lagrange equations can also be written as

Show that the Euler Lagrange Equations can also be written as $$\frac{\partial \dot{T}}{\partial \dot{q}_j} - 2\frac{\partial T}{\partial q_j}=Q_j$$
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1answer
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Find out the angular speed in terms of time.

Here is the equation that describes the motion of a planet under the gravitational field generated by a fixed star: $u=\frac el\cos\theta+\frac 1l$, where $u$ is the reciprocal of the radial distance ...
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2answers
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Confusion regarding ($d = rt$) vs ($x_1 = x_0 + v_o t + 0.5 at^2$) usage.

I'm following an online physics course and I can't understand why for the question below the equation distance = speed $\times$ time can't be used while the equation $x_1 = x_0 + v_0t + 1/2at^2$ can. ...
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1answer
46 views

Cross product for vector angular position?

The angular velocity of a particle $\omega = r \times v$ is a pseudovector because it is formed by the cross product of two vectors (position and linear velocity). Likewise the angular acceleration ...
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1answer
25 views

How does this differential equation solve to give this?

Hello I would like to see how this differential equation solves to give the result on the picture. $c$ is a constant and I believe $\frac{dm}{dt}=-k$ Obviously they are dividing by $m$ and then ...
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1answer
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Where is the error in this answer Newton's motion

I am asked to find the distance between the Earth and the Moon given only the constant $G$, the mass of the Earth and that it takes the Moon 28 days to orbit the Earth once as assumed. I said we have ...
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0answers
41 views

classic derivation of the proportionality between angular momentum and magnetic moment problem

The question is given in parentheses. It is a classic derivation of the proportionality between angular momentum and magnetic moment $m=-IA=-I\pi r^2$ We start with the charge on a ring (say, the ...
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0answers
45 views

complex potentials in plane polar coordinates - stream function

Determine the stream function and the potential in plane polar coordinates and sketching streamlines We need to take the value of m=1. I have an idea on how to do the parts and i know what a ...
0
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1answer
64 views

Vectors problem, Please Help!

A buoy is floating in water and is tied to a post. The water is creating a force of $3$ N on a bearing of $125^\circ$ and the wind is creating a force of $2$ N on a bearing of $230^\circ$ What force ...
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0answers
59 views

Attempt to solve the brachistochrone problem

I am attempting to solve the brachistochrone problem for fun. I don't have too much experience with differential equations and wanted to see if I am on the right path. My attempt Assumptions ...
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0answers
21 views

Oscillation of a disc about a rod perpendicular to the disc but not through the centre.

A thin uniform circular disc of radius a and centre A, with density p, has a circular hole cut in it of radius b and centre B, where $AB = c < a−b$. The disc is free to oscillate in a vertical ...
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2answers
37 views

Calculating a 3 way circle collision

I need to calculate the resultant velocities of 3 circles/masses/particles if they was to collide at the exact same time. I understand that this is theoretically impossible (or incredibly unlikely) to ...
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2answers
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Is the work integral decomposable?

Work is defined as $W = \int_{\gamma} \vec F \cdot d\vec l$ which I think means $W = \int (F_x, F_y, F_z) \cdot (dx, dy, dz)$. So by the linearity of the integral, could we always decompose work into ...
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1answer
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Curiosity with the Cartesian Notation of the Vector Cross Product

In my opinion Hibbeler's book on statics (Engineering Mechanics Statics, 12th ed) is one of the most approachable on the subject. On pg.123 he defines the Vector Cross Product in its Cartesian ...
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0answers
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Mechanics problem need to find expression for distance traveled.

Okay so I'm stuck on this problem. I have a ball that is projected at a cliff edge with a velocity $v$ and at an angle $\theta$ to the horizontal. The cliff edge is a height $h$ above the ground. The ...
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0answers
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Mechanics - Kinematics in two dimensions, how to find the time given a quadratic?

I have this information: $$u = 2i + 3j$$ $$r0(\text{initial position}) = 40i + 20j$$ $$r = 52i + 128j$$ $$a = -0.06i -0.04j$$ I need to find the $t(\text{time})$ at this point. I can use the equation ...
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0answers
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How to show the planet always stays in the same plane?

I know angular momentum $q \times p$ is conserved, where $p=L_{\dot q}$ is linear momentum. How to apply this to a planet orbiting the star, described by the position vector $q$ relative to the star. ...