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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 .

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Deriving an expression of kinetic energy

How is it that $$ mv\frac{dv}{dt} = \frac{d}{dt}\left(\frac{1}{2}mv^2\right) $$ I cannot seem to arrive at the expression, getting stuck at $$ \frac{d(mv^2)}{dt}=\frac{dm}{dt}v^2+2mv\frac{dv}{dt} $$
Roberto_1986
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Resolving Forces

A ball of weight $1\,\text{N}$ is placed on a slope $25°$ to the horizontal. Find the normal force experienced by the ball. I know this seems like a really simple question but I would normally take $R$ as $W\cos(25^{\circ})$ as it is perpendicular…
Arjun
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Why a set of coordinates and velocities can uniquely determine a mechanical system?

In the 1st page of Landau's "Mechanics", he used "known from experience" and "in principle" to state that a $N$-degree of freedom particle system is completely determined by $2N$ variables ($N$ generalized positions and $N$ generalized velocities)…
bruin
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Find how much longer it takes one runner to finish a race compared to another runner (velocity time graphs).

Peter and Sanjit are running in a race. They both start from rest. Peter accelerates uniformly, then moves at a constant speed v for 5 seconds and then decelerates uniformly, coming to rest at the finish line. Sanjit accelerates uniformly, at the…
Jamminermit
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Simple mechanics problem.

Question A train is travelling West to East along a straight horizontal track. A child suspends a pendulum from the roof of one of the carriages and notices that the pendulum is inclined at an angle of 4◦ to the vertical. Calculate the acceleration…
SFR
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Inducing circular motion problem

Suppose a planet is moving under the influence of the central force of a star. When it reaches its closest distance to the star (i.e. where $\dot{r}=0$) its velocity $\textbf{v}=\dot{r}\textbf{e}_r + r\dot{\theta}\textbf{e}_\theta$ is reduced by…
Azamat Bagatov
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Maximum displacement of finite string

If the transverse displacement of a string is given by $u(x,t)$, how would I go about calculating the maximum displacement of the midpoint of that string? Is this just when $u(x,t)$ is maximised? Where does the 'midpoint' come into it?
Azamat Bagatov
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particle attached to a string and projected

I'm stuck in the following question: One end of a light inextensible string of length $a$ is attacheded to a fixed point $A$, a distance $\frac{13a}{27}$ below a horizontal ceiling. The other end supports a particle which is projected from its…
amika patel
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How to model this problem as a boundary value problem of PDE system

I am trying to solve this system of elasticity partial differential equations in 2D in cylindrical coordinates, where the model is axysimmetric, around the $z$ axis. $$\frac{1}{r} \frac{\partial (r\sigma_{rr})}{\partial r} +\frac{\partial…
LejlaS
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Classical Rigid body Mechanics

A thin heavy disc can turn freely, about an axis in its own plane, and this revolves horizontally with a uniform angular velocity $\omega$ about a fixed point on itself. Show that the inclination $\theta$ of the plane of the disc to the vertical is…
Soumya Kanti Das
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Formula for crank/piston setup

I’m not totally certain how to ask this question or what mechanism this is, but I’m trying to know how far the bottom of a vertical object will travel when pushed straight down from the top. Excertion | | | |<——- What is diaganol…
Michael Rader
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In a pulley system involving two particles attached to the ends of a light, inextensible string...

if one particle descends by a certain distance, will the other particle ascend by the same distance? For example, if the two particles are hanging next to eachother, both 2 metres above the ground. If one of the particles descends by 2 metres, would…
Siddharth Chaudhary
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Pulley system - Tension and Reaction

I got this question and so far I think I have worked out the tension correctly. 2T = 5g + 4g T= 4.5g However I don't know how to proceed with the second part where it is asking the force exerted on B by ground. I think this would be the reaction…
user122343
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conservation of energy vs conservation of momentum different results

A pendulum of length $1$ m and mass $100$ g attached to the end. Another 100 g mass move horizontally with speed 2 m/s. When collision happens this ball sticks with the pendulum and move together. Find the initial linear speed of the…
Mahmoud Emad
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How to show equlibrium forces in two ladders leaning against each other, other ends resting on rough floor?

Two equal ladders of weight W each are placed so as to lean at A against each other with their ends resting on a rough floor, given the coefficient of friction is u. The ladders at A make an angle 2a with each other. Find what weight on the top…
Manvendra
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