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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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Friction between bead and wire

A smooth bead is threaded on a rough horizontal wire (coeff friction, u) and free to move along it. The bead is subject to the following forces: its weight W, F1 pulling it along the wire and F2 at right angles to F1 and W. Is the maximum frictional…
Quadratic Reciprocity
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A person of mass 80kg is standing in a lift of mass 600kg.

The lift is supported by a cable which is modelled as light and inextensible. The lift is moving upwards and decelerating at 1.8m.s⁻² a) Find the tension in the lift cable. b) Find the magnitude of the normal reaction exerted by the floor of the…
Kurosaki Ichigo
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Show that the vertical component of the reaction is constant

A smooth wire in the shape of the helix $\vec{r} = a (cos θ)\vec{i}+ a (sin θ)\vec{j}+ cθ\vec{k}$, where $a$ and $c$ are positive constants is fixed with the $z$-axis pointing vertically downwards. A bead of mass $m$, free to slide along the wire,…
ALMEra
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Problem based on Rigid Body Mechanics (Newtonian-Mechanics)

I got this problem in a tutorial sheet given to me by my Professor. I am confused as to how to apply the torque about point C, which is hinged. Please be kind to ignore any wrong format of asking the question. Without any further ado, Here's the…
P. Patil
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Find force of gravity

Material point describes an ellipse (with axes $a$ and $b$) under the action of force of gravity. At the end of bigger axis the velocity of point is equal to $v_0$. I need to find the force of gravity as a function of radius vector. So the force is…
Savva Zosimov
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How do I solve this question on Hooke's law?

A particle of mass $2$ kg is being held in equilibrium on a smooth slope by a horizontal force $p$ and a light elastic spring. The spring has modulus of elasticity $10$N and is attached to the particle and also to the slope $1.5$m up the slope from…
kaushik das
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Finding Lagrangian of a system (Oscillations in a parabolic trough)

A particle of mass m slides down on the curve $z=1+\frac{x^2}{2}$ in the $xz$-plane without friction under the action of constant gravity.Suppose $z$-axis points vertically upward.Find the Lagrangian of given system. The position vector of the…
Shreya Chauhan
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Euler–Lagrange for cabin on a Ferris wheel - solution with special function

I am looking for a special function which solves the equation of motion of a cabin on a Ferris wheel. The e.o.m. reads $$ \ddot{\phi} + a \, \sin\phi + b \, \sin(\phi - \tau) = 0 $$ with $$ a = gl^{-1}\Omega^{-2} $$ $$ b = Rl^{-1} $$ $$ \tau =…
TomS
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Cambridge Admissions Exam 1987 Paper

The problem I am attempting is the following I got pretty far into it, however, I was not able to do the last step of the solution. The given solution is here What I don't understand: I don't understand where the last equation comes from. Can…
Maths Wizzard
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Why does the centripetal force not given in the Equation (I)?

Example 4.1(An Introduction to Mechanics, 2E,Kleppner and Kolenkow) The Bola is used by gauchos for entangling their cattle. It consists of three balls of stone or iron connected by thongs. The gaucho whirls the bola in the air and hurls it at…
Unknown x
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Number of degrees of freedom of two particles connected by a rigid rod moving freely in a plane is?

Hi respected researchers and scholars, I have a question regading degrees of freedom Number of degrees of freedom of two particles connected by a rigid rod moving freely in a plane is _______ ? I have in my mind is: For a single particle it is 2 in…
Taj
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trajectory of block on incline

A block of mass m is kept at the lowest point on a wedge of mass $M$ of height $h$ and it has an angle of inclination $\theta$. The wedge accelerates with an acceleration $a$ such that the mass $m$ is accelerated up the incline. What will the…
sandy
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Derive this expression, relating to the range of a projectile

The range of a particle projected at an angle $\alpha$ from a horizontal plane, neglecting air resistance is $\dfrac{v_0^2sin(2\alpha)}{g}$. The particle falls short of the target by a distance of $a$. When the particle is projected at an angle…
Mathlete
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Differential equation of the central orbit

Why is $$h = v sin(\alpha) b$$, I know that h is a constant $$ = \frac{d\theta}{dt} r^2$$ but in every problem h is taken as the product of the starting velocity and the position and the sine of the angle of projection. In the same problem ,…
trytryandtry
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Impulse and change of direction

A particle $P$, of mass $0.5$ kg, is moving with velocity $(4i+4j)$ m/s when it receives an impulse $I$ of magnitude $2.5$ Ns. As a result of the impulse, the direction of motion of $P$ is deflected through an angle of $45^\circ$. Given that…
sdasd
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