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Questions tagged [classical-mechanics]

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question.

Wikipedia says:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include , , and .

2097 questions
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Mechanics question...

Particles P and Q are attached to opposite ends of a light in-extensible string. P is at rest on a rough horizontal table. The string passes over a small smooth pulley which is fixed at the edge of the table.Q hangs vertically below the pulley (see…
Salma
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Magnitude and Point of Application

Suppose there are vertical forces $P_1, P_2, \dots P_n$ that act at the points $A_1, A_2, \dots , A_n$ that are located in $xz$ plane. How can I find the magnitude and point of application of the resultant forces?
user3514748
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Velocity at which the second locomotive will catch the first without passing it?

For my first problem session in classical mechanics I got stuck on this problem about locomotive velocity. Here is the description: A locomotive leaves a train station with the magnitude of its displacement along a straight track given by $s=(1.4…
user7814
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Kinematics SUVAT Simultaneous Equation

I have the following question: A car accelerates for four seconds at a constant rate. Over the four seconds it travels 104m. It covered 58m in the last two seconds. Find the speed at which the car was traveling before it started to accelerate…
Joshua
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Why is the speed of a point of a one-end-fixed string dependent on its distance from the fixed end?

Problem. There is a uniform string with one end fixed to a peg, and the other end getting pulled away at a constant speed, say $u$. At time $0$, the string has length $a$ and is taut. At time $t$, a point of the string has a distance $x$ away from…
IncredibleSimon
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Old O level additional mathematics question on linear motion

Question reads as follows: A road runs alongside a railway line and a cyclist travels along the road at a uniform speed of $10 ~\text{m.p.h.}$ The driver of a goods train starts his train $5$ minutes after the cyclist passes him and the train…
GR L
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Using a parameterisation of Lagrangian and conserved quantities to reduce dimensionality

Nb. This is a past exam paper question I am attempting to answer Given the following Lagrangian $$\mathcal{L}=\frac{1}{2}mg_{ij}\dot x^{i}\dot x^{j}-U(x^4)+\lambda(g_{ij}x^ix^j-a^2)$$ $(a)$ Specify any continuous symmetries and use Noether’s theorem…
benmcgloin
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find the greatest weight that can be added to $B$ before $B$ starts to descend.

A light rope $AB$ passes over a rough circular cylinder, which is fixed with its axis horizontal. Bodies of weights $M$ and $m$ are attached at $A$ and $B$ respectively so that the ends of the rope hang in a vertical plane perpendicular to the axis…
ALMEra
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Mechanics- Polar Co-ordinates

Recently we were taught about uniform circular motion and polar co-ordinates. For our homework we got an assignment with the position vector of an ellipse, expressed with $t$ as time. e.g. $4 \cos(2t) \hat{i} + 3 \sin(2t) \hat{j}$ We haven't really…
Lars
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Condition for the stable equilibrium of hemisphere having a particle attached at to its rim and standing over a sphere

I have a heavy hemispherical shell of radius $a$ and a particle is attached to its rim at some point. The curved surface shell rests on a sphere of radius $b$ on its highest point. I have to show that whatever be the weight of the particle, the…
HARVEER RAWAT
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Centre of gravity question. Should an equilateral triangle be removed and if so why an equilateral?

I am really struggling with the last part of this question and would really appreciate some help. The question, regarding centres of gravity, is from an old O level text and reads as follows: $ABCD$ is a uniform square plate, of side $2a$, $M$ and…
GR L
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A point is moving along the curve $y = x^2$ with unit speed. What is the magnitude of its acceleration at the point $(1/2, 1/4)$?

A point is moving along the curve $y = x^2$ with unit speed. What is the magnitude of its acceleration at the point $(1/2, 1/4)$? My approach : I use the parametric equation $s(t) = (ct, c^2t^2)$, then $v(t) = s'(t) = (c, 2c^2t)$ and $a(t) = v'(t) =…
walter
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O level additional mathematics (applied), obtaining solutions in the correct order

This is a question from an old O level additional mathematics book by T A Humphreys (1967). It is given as follows: Strings of length 4 ft and 3 ft are attached to a fixed point O and to the ends A, B respectively of a rod 5 ft long and weighing 15…
GR L
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Why $\frac{dU}{d\theta}=0$ indicates equilibrium?

Question. My confusion comes from a problem and its solution (both partially). Here is the problem. Here is the solution. Now, what baffles me is the highlighted part in the solution; I do not understand it. My Attempt. I tried to understand the…
IncredibleSimon
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Incorrect exam question? A package moving up an inclined plane, find range of values of coefficient of friction

The following question was in a recent exam: A package P of weight $10$ N is moving up an inclined plane under the action of a horizontal force of magnitude $20$ N. The plane is inclined at angle $\alpha$ to the horizontal,…
Joseph
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