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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 - Friction

I'm confused by this question: ... After resolving forces, I got $T=20g\sin{60} + 0.4\cdot 20g\cos{60} = 209N $ However, this is the answer for part B. After looking through solutions, the minimum tension required is when the frictional force is…
Tobi
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Time for the run of a test trial of an electric car.

Trials are being undertaken on a horizontal road to test the performance of an electrically powered car. The car has a top speed of $V$. During a test run, the car moves from rest with uniform acceleration $a$ and brought to rest with uniform…
J132
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A light elastic spring hanging vertically with a mass attached to its lower end.

A light elastic spring has a natural length $a$ and modulus of elasticity $λ$. The energy stored in the spring when it is stretched is $$\frac{λx^2}{2a}$$ where $x$ is the extension. A light elastic spring of natural length $0.2m$ and modulus of…
J132
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Mechanical Power and time to Mechanical energy

I have these two sets of data, the first being a time stamp (ms) and the other being mechanical power (W). For each of these I have to work out the mechanical energy in KWh. 0 0 362 3.76 402 3.76 442 7.12 482 10.68 522 12.46 562 16.02 602…
RMRiver
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Orbits under central forces

A particle moves in a plane under a force, towards a fixed centre, proportional to the distance. If the path of the particle has two apsidal distances $a,b\ (a>b)$, then find the equation of the path.
user315483
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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 $r = {r_{Earth}} + z$) I am supposed to show the GPE near…
Ahmed
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How to derive the equilibrium length of a spring?

A straight wire rotates with constant angular speed $\omega$ about one of its end points (the origin $O$) in a horizontal plane containing $e_1$ and $e_2$. A bead of mass $m$ is free to slide along the wire, but is connected to $O$ by a spring…
johnny09
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Coefficient of friction of a triangular lamina $ABC$ on a rough horizontal table.

A uniform triangular lamina $ABC$ of weight $W$ newtons is right angled at $B$. $AB$ has length $0.6m$ and $BC$ has length $0.8m$ and the lamina rests in a vertical plane with $AB$ in contact with a rough horizontal table. A force of magnitude $P$…
J132
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Three equal rough cylinders on a horizontal plane.

Two equal rough cylinders are lying in contact with each other, with their axes parallel and horizontal, on a rough horizontal plane. A third equal cylinder is placed symmetrically on top of the other two. If equilibrium is about to be broken by the…
J132
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A square based pyramid on cube - methods for finding the centre of gravity.

A uniform solid body is constructed using a square-based pyramid mounted on a cube. If each edge of the solid has length $l$ show that the centre of gravity of the body lies within the cube is, $\frac {11l}{(24 + 4√2)}$from the base of the…
J132
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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 plane about a smooth fixed horizontal circular rod of…
guest10923
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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 happen, but that's beyond the point. Here is an…
Ryan Ramsden
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Mass density function verification in continuum mechanics

I'm having problems knowing where to go with this question: "Suppose that a certain material initially fills an open region $O \subseteq \mathbb{R}^3$, with $\Omega := [−1, 1]^3 \subset O$, so in particular the cube centered at zero with volume $8$…
Dan Burrows
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Show that $P=\frac{3W}{5+3\sin\theta -\cos\theta}$

I am stuck on the first part. Here is what I have done so far. First I resolved $P$ into $P\sin\theta$ and $P\cos$$\theta$. Then resolving in the horizontal plane, I obtained $F_a + P$$\cos\theta=N_b$. Then resolving vertically I obtained…
user140161
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Vector spaces and bundles in classical mechanics

My understanding so far is that if we have a manifold of coordinates, the velocity field is more generally called a tangent space $T_xQ$, further the space described by position and momentum is a co-tangent space $T_x^*Q$. The union of all the…
Janet the Physicist
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