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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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Object of unknown mass in simple harmonic motion...

An object with mass m in simple harmonic motion on a vertical spring is observed for 5 full oscillations. The time is measured to be 13 seconds. What is the angular frequency (3dp)? A previous experiment using a test mass shows the spring constant…
Penny
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A question about a pendulum moving in simple harmonic motion

For a 2.7kg mass oscillating in simple harmonic motion (spring constant: 360N/m) with an amplitude of oscillations measured at 3.4cm. How do I calculate the total mechanical energy, maximum speed and at what positive displacement, the mass has half…
Penny
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Particle in simple harmonic motion

I am given that a particle in simple harmonic motion has equation of motion $$m\ddot x=-kx$$ I'm told that the particle is at rest at $x=l$ at $t=0.$ I am asked to find the maximum acceleration of the particle. I know that this occurs when the…
MHW
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Center of Pressure of a Cone

A Cone whose vertical angle is $\pi/3$ has its lowest generator horizontal and filled with a liquid. Prove that the pressure on the curved surface is $\frac{W\sqrt{19}}{2}$, where $W$ is the weight of the liquid. From my view: I would also like to…
Soham
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Finding the reaction force for a motorbike on an banked curve

I'm studying mechanics and we were always taught that for a particle on an inclined plane, the reaction force $R = mg\cos\theta$. However in this mechanics module, under circular motion, when a motorbike/other object is on a smooth bend in a track,…
Tiernan Watson
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Finding the potential energy at a general point on an ellipse

I am given that $\mathbf{r}=acos(\omega t) \hat i+bsin (\omega t) \hat j.$ From this I am able to conclude using $\mathbf{F}=m\mathbf{a}$ that $\mathbf{F}=m \bigg(-a\omega^2 cos(\omega t) \hat i -b\omega^2 sin(\omega t) \hat j \bigg).$ I am also…
MHW
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Mechanics Impulse Find mass of the bullet

A marksman fires a bullet from a gun with a horizontal speed of $360ms^{-1})$ The mass of the gun is $3kg$. The gun recoils into the marksman's shoulder with a horizontal speed of $6ms^{-1}$. Find the mass of the bullet. The gun comes to rest after…
StrangeApple
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How to find the time to reach the centre with increasing acceleration

A mass starts from rest at a distance a from the centre of force which attracts inversely as the distance. Find the time to reach the centre Here acceleration is inversely proportional to the distance and initial velocity is zero. But the…
user69468
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What is this dynamics question asking me to do?

I've made it to the the final part of this question and got the expression with arctan in it: However, I'm not sure what the final part is asking me to do. I know I've got to plug the new values into the right places, but I'm not sure what the end…
Trev
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Using the path equation to determine the orbit of a satellite.

A satellite is in a circular orbit a distance $h$ above the surface of the earth with speed $v_0$. It suffers a head-on collision with some debris which reduces its speed to $kv_0$, where $k$ is a constant in the range $0
user197848
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Trajectory intesection with itself

I would like to ask the following. I do know that if all the prerequisites of the Existence and Uniqueness theorem are satisfied, then a trajectory in the Euclidian space-time: \begin{equation} x(t)=(x_1(t), x_2(t),x_3(t)) \end{equation} is not able…
Bazinga
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Magnitude and direction of the force exerted by the wall on a rod smoothly hinged at its end on the wall.

A uniform rigid rod $AB$ has length $2\text{m}$ and weight $60\text{N}$. The rod is smoothly hinged at its end $A$ to a vertical wall. The rod is held at an angle of $60^\circ$ downward from the wall by a force of magnitude $F$ $\text{N}$ acting at…
J132
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A book resting in equilibrium on a horizontal shelf and against a wall.

A book is resting in equilibrium on a horizontal shelf and against a vertical wall, and makes an angle $\theta$ with the horizontal. A horizontal force of magnitude $P$ newtons is applied at the bottom right edge of the book (half way between the…
J132
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Uniform lamina (equilateral triangle) in a hoop.

A uniform lamina is in the shape of an equilateral triangle $ABC$, and rests in equilibrium inside a vertical circular hoop with $B$ and $C$ in contact with the hoop, and $A$ at the centre of the circle. Contact is smooth at $C$ and rough at $B$,…
J132
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Height of feed in a trapezoidal trough.

A trough has a cross-section in the form of a trapezium. Its base has a length of $1m$, and the sides slope out at $45^o$. to the horizontal. The trough is filled with feed to a depth of $xm$. Find the value of $x$ given that the centre of mass of…
J132
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