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classical mechanics | Dynamics of controlled overdamped inverted pendulum | https://physics.stackexchange.com/questions/69438/dynamics-of-controlled-overdamped-inverted-pendulum | <p>I wonder how to properly write the motion equations for the inverted pendulum on a cart in case of overdamped dynamics. Imagine the system <a href="http://en.wikipedia.org/wiki/Inverted_pendulum#Inverted_pendulum_on_a_cart" rel="nofollow noreferrer">illustrated in Wikipedia</a> placed in a liquid with high viscosity... | <p>Using $\sum F=m a$ and $\sum M = I \ddot{\theta}$ I arrive at</p>
<p>$$ F = \left( \frac{M+m}{m} \frac{I+m L^2}{L \cos\theta} - m L \cos \theta \right) \ddot{\theta} + \left( \frac{M+m}{m} \frac{\beta \dot\theta}{L \cos\theta} + m L \sin\theta \dot{\theta}^2 \right) $$</p>
<p>now you can play with the values to g... | 0 |
classical mechanics | The mighty man and the bridge | https://physics.stackexchange.com/questions/69984/the-mighty-man-and-the-bridge | <p>Let us say we have a mighty man crossing a bridge, carrying 4 bags of concrete, each of which weighs 50 pounds. </p>
<p>Let us say, for the sake of the argument, that the mighty man himself weighs 300 pounds.</p>
<p>The support capacity of the bridge $x$ is less than the 500 pounds they weigh together - therefore... | 1 | |
classical mechanics | Why doesn't Newton's Second Law include higher-order mass? | https://physics.stackexchange.com/questions/93659/why-doesnt-newtons-second-law-include-higher-order-mass | <p>I suspect this has been asked here before, but I didn't find anything using Search.</p>
<p>Why is Newton's second law only second-order in position? For instance, could there exist higher-order masses $m_i$ with</p>
<p>$$F(x) = m\ddot{x} + \sum_{i=3}^{\infty} m_i x^{(i)}?$$</p>
<p>Are there theoretical reasons wh... | <p>I think Newton's first law, linearity of motion, and the time-reversal symmetry strongly constrain the form of Newton's second law.</p>
<p>Generically, the linear relation between the position and the force is given by</p>
<p>$$
F = \beta_0 x+ \beta_1 \frac{dx}{dt} + \beta_2 \frac{d^2x}{dt^2} + \beta_3 \frac{d^3x}... | 2 |
classical mechanics | Is it possible to control a treadmill's tread speed such that a plane on the treadmill will be prevented from moving? | https://physics.stackexchange.com/questions/32325/is-it-possible-to-control-a-treadmills-tread-speed-such-that-a-plane-on-the-tre | <p>I've posed the question in this particular way to avoid the ambiguity usually found in the posing of the "<a href="http://pogue.blogs.nytimes.com/2006/12/11/the-airplane-treadmill-conundrum/" rel="nofollow noreferrer">airplane on a treadmill</a>" puzzle, <a href="https://physics.stackexchange.com/questions/32269/wha... | <p>yes it is possible. You have to account for the <strong>Tire Friction</strong> and <strong>Rolling resistance</strong>. It is a bit complicated math but you can resort to experiment. Attach a spring balance to the nose and measure the resistance offered by the tires while the treadmill is spinning at desired speed. ... | 3 |
classical mechanics | Why are bricks typically constructed to have six faces at, or near right-angles to each the other? | https://physics.stackexchange.com/questions/32911/why-are-bricks-typically-constructed-to-have-six-faces-at-or-near-right-angles | <p>Looking around it appears that bricks, through history, have been constructed in cuboid form i.e. with six faces at right-angles to each other. This is also apparently the case with stone construction too - six-sided volumes.</p>
<p>Is the cuboid form the most efficient form to bear load? </p>
<p>How do other form... | <p>Since I argued to re-open this question I should put the effort in to answer it :)</p>
<p>As other answers have pointed out, there <em>are</em> important cultural reasons why we use cubical bricks, and different architectural traditions may predominantly use bricks of different shapes. Not all bricks are cuboid - i... | 4 |
classical mechanics | On the Discretization of Energy Levels | https://physics.stackexchange.com/questions/34447/on-the-discretization-of-energy-levels | <p>We consider a system of "n" particles whose total energy E and net momentum $\vec{P}$ are fixed are fixed.There no net force on the system(assumed)</p>
<p>$$\Sigma \epsilon_i= E$$
$$\Sigma\vec{p_i}=\vec{P}$$
For an individual particle its momentnum and energy remain constant for the time $\tau$,the relaxation time(... | <p>This is nonsense--- the "quantization of energy" you are referring to in classical theories is not a quantization at all, it is equipartition. It is only true that independent degrees of freedom have an average energy which is roughly quantized in classical mechanics.</p>
<p>You can't make a classical equilibrium b... | 5 |
classical mechanics | How does a treadmill incline mechanism work? | https://physics.stackexchange.com/questions/35313/how-does-a-treadmill-incline-mechanism-work | <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://physics.stackexchange.com/questions/1639/whats-the-difference-between-running-up-a-hill-and-running-up-an-inclined-tread">What's the difference between running up a hill and running up an inclined treadmill?</a> </p>
</blockquote>
<p>... | 6 | |
classical mechanics | Complex part of the solution for physical values | https://physics.stackexchange.com/questions/35805/complex-part-of-the-solution-for-physical-values | <p>What's a physical meaning of, for example, complex part of the solution for coordinate change of the anharmonic oscillator?
Why after substitute (for diff. equation solve) for real x we can earn $x = Re(z) + iIm(z)$? It's because of substitute?</p>
| <p>When we wish to solve a differential equation like your example, a good guess for when $f(t)=0$ is something of the form $x(t) = e^{i \alpha t}$. This just gives us an algebraic equation for $\alpha$, which we can just solve. I interpret your question to mean: but what is this solution? Why is it complex? Indeed, po... | 7 |
classical mechanics | Formulas for compressibility of solids (physics) | https://physics.stackexchange.com/questions/38246/formulas-for-compressibility-of-solids-physics | <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://physics.stackexchange.com/questions/37571/formulas-for-compressibility-of-solids">Formulas for compressibility of solids</a> </p>
</blockquote>
<p>I have a question which is technically a physics question, but since I have yet to find a g... | 8 | |
classical mechanics | all the 1-dimensional problems in newtonian mechanics are solvable? | https://physics.stackexchange.com/questions/51774/all-the-1-dimensional-problems-in-newtonian-mechanics-are-solvable | <p>i mean given a system with a conserved Energy in one dimension</p>
<p>$$ E= \frac{p^{2}}{2m}+V(x) $$</p>
<p>then the 'solution' to this problem is implicitly given by</p>
<p>$$ t(x)= \frac{1}{2m} \int_{0}^{x}\frac{du}{\sqrt{E-V(u)}} $$</p>
<p>so apparently from this equation we could know all the quantities $ p(... | <p>Yes, and generally it is solvable numerically just like a differential equation of motion is generally solvable numerically.</p>
| 9 |
classical mechanics | Total Mechanical Advantage | https://physics.stackexchange.com/questions/51615/total-mechanical-advantage | <p>How do you find the net <a href="http://en.wikipedia.org/wiki/Mechanical_advantage" rel="nofollow">Mechanical Advantage</a> (MA) of two joint machines. Do you add or multiply the individual MA?</p>
<p>Suppose I have two sets of wheel and axle connected by a fixed pulley. Each of the wheel has a radius of 100cm and ... | <p>It is multiplication.</p>
<p>When you turn the wheel at the beginning by $x$ degrees, the axle at the end will turn by $x/100$ degrees. This comparison of lengths/angles of movement directly translates to the mechanical advantage. The work is a constant, so because of $W=x_1 F_1=x_2 F_2=x_1/100 F_2=x_1/100\cdot 100... | 10 |
classical mechanics | What does net mechanical efficiency mean? | https://physics.stackexchange.com/questions/52697/what-does-net-mechanical-efficiency-mean | <p>I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for example: <code>... increased the effectiveness, while reducing net mechanical efficiency.</code> What does exactly does thi... | <p>Mechanical efficiency is usually used as a metric to account for frictional losses in systems. For example, the transmission of a car transmits mechanical work from the engine to the wheels so the mechanical efficiency of the system will be $W_{transmitted}/W_{received/ideal}$. Even within an engine, there is fricti... | 11 |
classical mechanics | Lego Blender and gear ratios | https://physics.stackexchange.com/questions/56557/lego-blender-and-gear-ratios | <p>I bought the Lego Kit LEGO Crazy Contraptions. It allows the learner to build a blender. My son, the engineer, said something to our grandson, his son, about a gear ratio. Can someone translate?</p>
| <p>A blender spins very fast, presumably faster than the motor supplied in that kit. A gear is a pair of cogs which mesh together to change the rotation speed. If a cog with 20 teeth meshes with one with 10 teeth, then for every 1 turn of the large cog, the small cog will turn twice. This is known as a 1:2 gear ratio, ... | 12 |
classical mechanics | what's the center of mass for triatomic-molecule system | https://physics.stackexchange.com/questions/60963/whats-the-center-of-mass-for-triatomic-molecule-system | <p>My text use the following example to explain the center of mass. There are three balls (mass $m$) sitting in the origin, at $x=l$ and $x=2l$, each two mass are connected with a spring of constant $k$. The system can only move along $x$ direction. To find the center of mass, I setup the coordinate system with first b... | <p>The center of mas is not what you have defined, the center of mass is:</p>
<p>$$
x_{com}= \frac{mx_1 + mx_2 + mx_3 }{m+m+m} = \frac{x_1 + x_2 + x_3 }{3}
$$ </p>
<p>and if we use $x_1 = 0$, $x_2=l$, $x_3=2l$:</p>
<p>$$
x_{com}= \frac{0 + l + 2l}{3} = l
$$ </p>
<p>acording with your geometrical aproach. </p>
| 13 |
classical mechanics | if a simple pendulum is dropped in a elevator with a acceleration greater than acceleration due to gravity then what will be its frequency | https://physics.stackexchange.com/questions/65107/if-a-simple-pendulum-is-dropped-in-a-elevator-with-a-acceleration-greater-than-a | <p>if a simple pendulum is dropped in a elevator with a acceleration greater than acceleration due to gravity then what will be its frequency ? We know time period depends on frequency.</p>
| <p>Same formula as usual but with the difference that. $$ g\rightarrow g\pm g'$$ where $g'$ is the acceleration of the elevator. The plus sign is used if the two accelerations are in different directions... Thus if elevator free fall then $g-g'=0 $ and the period goes to infinity. </p>
| 14 |
classical mechanics | Convert running speed uphill to equivilent speed on flat | https://physics.stackexchange.com/questions/5882/convert-running-speed-uphill-to-equivilent-speed-on-flat | <p>Given a certain running pace uphill, I want to be able to determine an equivalent pace running with no elevation change. Assumptions: similar effort in both cases (say for example running at 90% max heart rate), ignore wind, slope is constant for simplicity, ignore physiological and bio-mechanical factors, weight of... | <p>The easiest (and roughest) way to to do it would be to convert your running "work" into a VO2 score. </p>
<p>The American College of Sports Med's equation is </p>
<p>VO2= Resting Component + Horizontal Component + Vertical Component
or VO2= 3.5 + (0.2 x Speed) + (0.9 x Speed x Elevation Gain)</p>
<p>So, using you... | 15 |
classical mechanics | Name of the guy that Feynman mentioned during a lecture: the diagram is of a chain hanging over a triangle | https://physics.stackexchange.com/questions/12792/name-of-the-guy-that-feynman-mentioned-during-a-lecture-the-diagram-is-of-a-cha | <p>In a Feynman book, he talks about a man (I believe he lived 400-500 years ago) that discovered something about the dimensions of triangles (I think)by hanging a chain around the triangle. I've searched in "Six Not So Easy Pieces" but haven't been able to find it.</p>
<p>I'm trying to find the name of this man; it ... | <p>I think it may be Simon Stevin. He lived in years 1548–1620 and did put chain around triangle, which helped him study equilibrium of forces on inclined plane. </p>
<p>This is Wikipedia article about him: <a href="http://en.wikipedia.org/wiki/Simon_Stevin">http://en.wikipedia.org/wiki/Simon_Stevin</a></p>
| 16 |
classical mechanics | kinetic energy and conservative force field | https://physics.stackexchange.com/questions/13878/kinetic-energy-and-conservative-force-field | <p>The kinetic energy of a particle is a periodic function in time. Does it imply that the particle is in a conservative force field and there are no dissipative forces acting on it at any instance of time ?</p>
<p><strong>EDIT</strong> (in view of comment by Willie)</p>
<p>Please consider the question as "Is the for... | <p>No. I can take a ball and swing it back and forth periodically with my hand. The motion is periodic, but the situation is not conservative - my body generates a lot of heat.</p>
<p>A simple mathematical example is <a href="http://farside.ph.utexas.edu/teaching/315/Waves/node12.html" rel="nofollow">a forced, dampe... | 17 |
classical mechanics | Confusion with the torque | https://physics.stackexchange.com/questions/14080/confusion-with-the-torque | <p>Consider an imaginary vertical plane. Now say, a body is falling freely (under earth's attraction). If you consider any axis that is perpendicular to that plane. We get a non-zero value for torque. Then why is it that body is not moving in a circular path about that axis?</p>
| <p>When you exert a torque on something, its angular momentum changes. This doesn't necessarily mean things are moving in a circle, or even rotating. You can have torque and changing angular momentum even when things are going in a straight line. </p>
<p>Most of the time, when we discuss torque and angular momentum... | 18 |
classical mechanics | What does this infinitesimal Eulerian change describe? | https://physics.stackexchange.com/questions/16279/what-does-this-infinitesimal-eulerian-change-describe | <p>This is a question I originally <a href="https://math.stackexchange.com/questions/70746/what-does-this-infinitesimal-eulerian-change-describe">posted</a> in math.se which received an answer that was far too mathematically sophisticated for what I wanted; given that basic multivariable calculus was used through out t... | <p>This is a hard question, because Thomas is using terrible language. Most of the same calculation is done easily in my answer to this question: <a href="https://physics.stackexchange.com/questions/14751/how-did-l-h-thomas-derive-his-1927-expressions-for-an-electron-with-an-axis">How did L.H. Thomas derive his 1927 ex... | 19 |
classical mechanics | How should a closed-ended terrestrial trajectory be corrected for the Coriolis effect? | https://physics.stackexchange.com/questions/17342/how-should-a-closed-ended-terrestrial-trajectory-be-corrected-for-the-coriolis-e | <p>I have tried verifying the numerical integration of the Coriolis effect for 1000 to 2000-yard rifle fire by switching ON/OFF the Coriolis correction of a good ballistic simulator program (PRODAS). The program integrates an instantaneously evaluated Coriolis acceleration along with the aerodynamic and gravitational a... | <p>The cumulative Coriolis effect must be <em>independent of the path</em> between the two end-points of the flight segment to which it applies. The Coriolis effect is entirely due to the motion of the observer and not to that of the object. Direct integration of the instantaneous Coriolis acceleration over a curved tr... | 20 |
classical mechanics | How fast will the projectile go the second time? | https://physics.stackexchange.com/questions/19395/how-fast-will-the-projectile-go-the-second-time | <p>Say I have a linear motor [aka rail-gun] and use a x amount of electrical power. I fire the gun and the object exits at velocity v. I then reuse the same object as my projectile and fire the rail-gun a second time this time with 2x the electrical power. My lessons on momentum suggest it will go 2v. The Work-Ener... | <p>Your railgun has some fixed length. If you apply some voltage to generate some force, then the energy gained by the projectile will simply be force times distance (i.e. the length of the railgun).</p>
<p>If you now double the voltage, to get twice the force, the work done will be twice as great so the projectile wi... | 21 |
classical mechanics | Does mass affects accelleration of an object in a sloapy movement? | https://physics.stackexchange.com/questions/19548/does-mass-affects-accelleration-of-an-object-in-a-sloapy-movement | <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://physics.stackexchange.com/questions/19552/would-a-light-or-a-heavy-ball-roll-fastest-down-a-slope">Would a light or a heavy ball roll fastest down a slope?</a> </p>
</blockquote>
<p>Is there a change of the accelleration of an object movi... | 22 | |
classical mechanics | Does a straight water hose issue water at a greater pressure than a Coiled water hose of same diameter and length? | https://physics.stackexchange.com/questions/20656/does-a-straight-water-hose-issue-water-at-a-greater-pressure-than-a-coiled-water | <p>I have a one BHP water pump, the water pressure of a coiled hose connected to the water pump output side was not that great. Would an unwound water hose produce greater water pressure? [Friction Losses?]</p>
<p>Thanks,
Alan</p>
| <p>Yes, but under normal circumstances (e.g. garden hose scale) you wouldn't notice.</p>
<p>Friction losses are higher in bends, especially sharp bends, but the coils in a regular hose aren't very sharp. This is by design: hoses are made fairly sturdy so you don't get unintentional sharp bends. So it's really down to ... | 23 |
classical mechanics | Numerical torque calculation | https://physics.stackexchange.com/questions/29022/numerical-torque-calculation | <p>Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically compute force acting on the center of mass of the body by calculating numerical derivatives e.g. $F_x = (E(x + dx) - E... | <p>OK. I found the answer:</p>
<p>$$
\partial V/\partial \theta = N_x \cos \psi - N_y \sin \psi
$$
$$
\partial V/\partial \phi = N_x \sin \theta \sin \psi + N_y \sin \theta \cos \psi + N_z \cos \theta$$
$$
\partial V/\partial \psi = N_z
$$</p>
<p>Where $\theta, \psi, \phi$ are Euler angles and $N_x, N_y, N_z$ are Tor... | 24 |
classical mechanics | Path traced out by a point | https://physics.stackexchange.com/questions/30614/path-traced-out-by-a-point | <p>While studying uniform circular motion at school, one of my friends asked a question:</p>
<p>"How do I prove that the path traced out by a particle such that an applied force of constant magnitude acts on it perpendicular to its velocity is a circle?" Our physics teacher said it was not exactly a very simple thing... | <p>One can prove it in a more-or-less elementary way by solving a pair of simultaneous differential equations. In two dimensions, a vector that is perpendicular to a velocity $$\left(\begin{matrix}u(t)\cr v(t)\end{matrix}\right)\quad\mathrm{is}\quad\left(\begin{matrix}-v(t)\cr u(t)\end{matrix}\right).$$ The acceleratio... | 25 |
classical mechanics | Ball bouncing elastically off a wall with no slipping | https://physics.stackexchange.com/questions/440212/ball-bouncing-elastically-off-a-wall-with-no-slipping | <p>I am a bit confused about what seems like it should be a perfectly straightforward problem in mechanics with a well defined solution.</p>
<p>A sphere approaches a wall from an angle and rebounds elastically. The coefficient of static friction between sphere and wall is large—no slipping occurs during the brief peri... | <p>I'll give here the 2D version of my answer to <a href="https://physics.stackexchange.com/a/429834/197851">this question</a> since there's no guarantee that question (having been closed) won't disappear at some point.</p>
<p>If the wall is in the <span class="math-container">$x$</span> direction, as you suggested, l... | 26 |
classical mechanics | Invariance of Space and Time in Different Reference Frames | https://physics.stackexchange.com/questions/451280/invariance-of-space-and-time-in-different-reference-frames | <p>I'm studying dynamics by Anil Rao's book. He said something that made me really confused. The citations below construct the problem.</p>
<blockquote>
<p>[...]</p>
<p>An assumption of Newtonian mechanics is that space is invariant with
respect to changes in reference frames, i.e., observations made of
space are the s... | 27 | |
classical mechanics | Does the axis of rotation of a rigid body depend on the frame of reference? | https://physics.stackexchange.com/questions/452360/does-the-axis-of-rotation-of-a-rigid-body-depend-on-the-frame-of-reference | <p>When studying the kinematic motion of a rigid body, angular velocity <span class="math-container">$\omega$</span> is a vector that not seem to specify a unique axis of rotation... When looking at the free rigid body motion of a wheel rolling without sliding, we can talk about the wheel's rotation from the point of ... | <p>I don't understand the question.</p>
<p>At any instance, in any <em>one</em> coordinate frame if the position <span class="math-container">$\boldsymbol{r}_A$</span>, velocity <span class="math-container">$\boldsymbol{v}_A$</span> of a point <strong>A</strong> in a rigid body rotating with <span class="math-container... | 28 |
classical mechanics | Linear acceleration on a spinning satellite with an unbalanced force | https://physics.stackexchange.com/questions/510025/linear-acceleration-on-a-spinning-satellite-with-an-unbalanced-force | <p>If there is a satellite in orbit in space, with an off centre booster providing an unbalanced force, it will experience rotational acceleration. However, I was wondering if it also undergoes linear acceleration while spinning, or only for a brief moment at the start...</p>
| <p><img src="https://i.sstatic.net/2mea2.png" alt="Force divided into components"></p>
<p>Here I have drawn a simple diagram of what might answer your question. <span class="math-container">$\overrightarrow{a}$</span> is the acceleration provided by the off-centred booster. <span class="math-container">$\overrightarro... | 29 |
classical mechanics | How does a drop of water evaporate and still maintain its drop shape? | https://physics.stackexchange.com/questions/534574/how-does-a-drop-of-water-evaporate-and-still-maintain-its-drop-shape | <p>Let's say we have a drop of water on a surface. Its surface tension maintains the shape. But was the water evaporates, the molecules leaving it, leave from the surface. Shouldn't the evaporation disturb the surface tension causing the water droplet to fall apart?</p>
| <p>As the drop gets smaller the ratio of the number of molecules on the boundary compared to those in the main volume gets higher. A smaller drop creates a stronger sphere. </p>
<p>As an exiting molecule leaves the boundary the molecules that were holding it in place lose the outward pull of that molecule and so becom... | 30 |
classical mechanics | Box Sliding Down an Inclined Plane - Underlying Assumption | https://physics.stackexchange.com/questions/546228/box-sliding-down-an-inclined-plane-underlying-assumption | <p>The classic introductory mechanics problem considers the motion of a box sliding down an inclined plane. As I'm reviewing the early chapters in Taylor's <em>Classical Mechanics</em>, I was struck by a question: in such a problem, we always <em>say</em> that the box has no motion in the y-direction (as is standard fo... | <p>The forces on the box in such questions are gravity, friction, and the reaction of the plane. The reaction of the plane is the key. Gravity has a component in the y direction, and would cause the object to fall through the plane if not for the reaction. </p>
<p>The plane is a rigid object. That means when a force t... | 31 |
classical mechanics | Conservation of Energy Question (train example) | https://physics.stackexchange.com/questions/581827/conservation-of-energy-question-train-example | <p>So we have a train going 5 m/s that gets loaded with 20,000 kg of coal while going over a 10m platform for 2 s. There is a 50,000 N horizontal force applied to the train during that period in order to keep the train going a constant 5 m/s.</p>
<p>That 50,000 N force does 500,000 J of work. But the KE of the coal at ... | <p>The addition of coal essentially constitutes as a series of inelastic collisions. Therefore, kinetic energy will be lost. The energy loss comes from work done by internal forces between the coal and the train.</p>
| 32 |
classical mechanics | Coordinate transformation to non-inertial frame: do we assume displacement is invariant? | https://physics.stackexchange.com/questions/658470/coordinate-transformation-to-non-inertial-frame-do-we-assume-displacement-is-in | <p>I'm a math student who's studying classical mechanics for the first time, so forgive me if this question sounds pedantic, but I find it hard to think about such problems without stating assumptions clearly.</p>
<p>If a frame K' is accelerating away from an inertial frame K, we wish to transform from the inertial to ... | <p>The primary assumption that you are talking about: I like to call that the 'inertial dead reckoning' assumption.</p>
<p>So the metaphor is 'dead reckoning'.<br />
Quick recapitulation of 'dead reckoning'.<br />
Two ships are on a motionless body of water. The two ships depart from each other, both keep an exact log ... | 33 |
classical mechanics | Particle collides with hard wall | https://physics.stackexchange.com/questions/716422/particle-collides-with-hard-wall | <p>When a particle elastically collides with a hard wall at some velocity, can the point at which the particle instantenously jumps be assumed to have zero velocity for potential to be continuous?</p>
| <p>Assuming a head-on collision (or only considering the normal component of the velocity), we could apply the <a href="https://en.wikipedia.org/wiki/Mean_value_theorem" rel="nofollow noreferrer">mean value theorem</a> to argue as follows: If velocity is given as <span class="math-container">$v(t) = dx(t)/dt$</span> wh... | 34 |
classical mechanics | Can a physical system have initial velocity zero, but non-zero constant everywhere else? | https://physics.stackexchange.com/questions/716442/can-a-physical-system-have-initial-velocity-zero-but-non-zero-constant-everywhe | <p>Does there exist a particular physical system where the initial velocity can be zero, but non-zero constant everywhere else?</p>
| <p>If the velocity is constant the force is zero. So we want a system which produces a very high force in an infinitesimally short time at <span class="math-container">$t=0$</span> and then drops back to zero. The simplest system that I can come up with right now is an ideal<span class="math-container">$^*$</span> bill... | 35 |
classical mechanics | Isn’t $(c^2 - v^2/c^2)^(1/2)$ the mathematical equivalent of $( 1 - v^2/c^2)^(1/2)$ ? Why do we never see it? | https://physics.stackexchange.com/questions/730910/isn-t-c2-v2-c21-2-the-mathematical-equivalent-of-1-v2-c21 | <p>Isn’t <span class="math-container">$\sqrt{c^2 - v^2/c^2} $</span> the mathematical equivalent of
<span class="math-container">$\sqrt{1 - v^2/c^2}$</span>? Why do we never see it presented this way?</p>
| <p>Are you asking why we never see <span class="math-container">$\sqrt{\frac{c^2-v^2}{c^2}}$</span> as opposed to <span class="math-container">$\sqrt{1-\frac{v^2}{c^2}}$</span>?</p>
<p>If so, what advantage does the former have? The latter expression makes it clear that the relevant quantity is <span class="math-conta... | 36 |
classical mechanics | Why may tensions calculated in different ways be slightly different? | https://physics.stackexchange.com/questions/213262/why-may-tensions-calculated-in-different-ways-be-slightly-different | <p>An question I am doing gives this situation:
<img src="https://i.sstatic.net/EMo57.jpg" alt="enter image description here"></p>
<p>Mass1 is 4kg. And mass2 is 7kg. </p>
<p>I expect the tension to be the same, no matter which mass I use in the calculation. But...</p>
<p>a=5.17</p>
<p>T1=7(9.81-5.17)=32.48N (whic... | <p>The two objects are connected by a string, and should therefore have the same acceleration. Based on some of the equations you are showing, I believe that object 1 is subject to friction with a coefficient of 0.3. We can then write the equations for the forces:</p>
<p>$$F_1 = T - m_1 g \mu\\
F_2 = m_2 g - T\\
a_1 =... | 37 |
classical mechanics | Friction of a rolling cylinder | https://physics.stackexchange.com/questions/214643/friction-of-a-rolling-cylinder | <p>I was wondering why friction vectors are drawn differently regarding a cylinder rolling on a surface and a cylinder rolling down an inclined surface. Since friction is responsible for the rotational motion shouldn't it be always pointing in the same direction (given that the cylinder is rotating to the right)?</p>
... | <p>This is because static friction, in the second case, tries to oppose the force which would otherwise result in the movement of the cylinder, which is the component of gravitational force along the inclined plane.</p>
<p>In the second case, I will assume that the rolling friction has been referred to. Then, the sho... | 38 |
classical mechanics | Again, why is kinetic energy and velocity independent of position coordinates in Cartesian coordinates | https://physics.stackexchange.com/questions/233073/again-why-is-kinetic-energy-and-velocity-independent-of-position-coordinates-in | <p>This might be a very simple question. I read one previous post
<a href="https://physics.stackexchange.com/questions/231185/can-the-kinetic-energy-be-a-function-of-the-position-vector">Can the kinetic energy be a function of the position vector?</a></p>
<p>I know that in Cartesian coordinates, the kinetic energy $T... | <p>In classical mechanics calculate the evolution of a particle means to know its position and its velocity for any time.</p>
<p>In general if I say that a particle is in position $x$ and has velocity $v$ and ask you about the kinetic energy. That is $\frac{1}{2}mv^2$ and this is independent of the system you have. Th... | 39 |
classical mechanics | Moving a Car the quickest path | https://physics.stackexchange.com/questions/240156/moving-a-car-the-quickest-path | <p>I have a car, that has a current angle and location, and a destination angle and location. The car has a maximum linear and angular acceleration. Assume the car will always travel in the direction it is facing. I'm trying to figure out how to determine the path that this car should travel that will be the quickest p... | 40 | |
classical mechanics | Sliding sphere wear shape | https://physics.stackexchange.com/questions/267665/sliding-sphere-wear-shape | <p>Please refer to the figure attached. Consider a normal force is acting on the top of sphere. A constant coefficient of friction causes frictional force throughout the sliding. I want to know after this sphere slides (pure sliding no rolling) for sometime and assuming that it wears as it slides, what should be the sh... | <p>Given the diagrams you present, I believe a straight wear(A) on the sphere is most likely. If the hardness of the surface is less than that of the sphere, there should be no, or almost no, wear on the sphere. </p>
<p>(b) Would primarily occur if your surface was curved, such as if it were U shaped or in the case ... | 41 |
classical mechanics | Is this a metorite captured on film or a bird/plane etc? | https://physics.stackexchange.com/questions/304770/is-this-a-metorite-captured-on-film-or-a-bird-plane-etc | <p>It is a shiny object in broad daylight, the distance seems quite far away, is there sufficient information in the footage to ascertain if it is a meteorite captured on film or something else?</p>
<p><a href="https://i.sstatic.net/PC3gE.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PC3gE.gif" alt="... | 42 | |
classical mechanics | Transport Theorem in analytical dynamics: basis of the vectors | https://physics.stackexchange.com/questions/399424/transport-theorem-in-analytical-dynamics-basis-of-the-vectors | <p>If we have two reference systems, <span class="math-container">$N$</span> and <span class="math-container">$B$</span>, with common origins <span class="math-container">$O_N=O_B$</span> and <span class="math-container">$B$</span> being rotating around <span class="math-container">$N$</span> with angular velocity <sp... | <p>We could rewrite the equation in the following way:</p>
<p><span class="math-container">$$\frac{d ({}^{B}\vec{u}) }{dt}\Biggr\rvert_N=\frac{d ({}^{B}\vec{u}) }{dt} \Biggr\rvert_{B}+ ({}^{B}\vec{\omega}_{B|N}) \wedge ({}^{B}\vec{u}) $$</span></p>
<p>The angular velocity vector <span class="math-container">$\vec{\omeg... | 43 |
classical mechanics | How does the actual elimination of dependent coordinates takes place? | https://physics.stackexchange.com/questions/601508/how-does-the-actual-elimination-of-dependent-coordinates-takes-place | <p>In the textbooks of classical mechanics I have been through, it is often quoted that, given an <span class="math-container">$N$</span> particle system having <span class="math-container">$3N$</span> Cartesian coordinates <span class="math-container">$(x_i,y_i,z_i)$</span> connected by <span class="math-container">$r... | <p>you forgot in your equations the constraint forces:</p>
<p>for the free body diagram (1 particle) with constraint equations you obtain:</p>
<p><span class="math-container">$$m\ddot x=F_x+F_{cx}$$</span>
<span class="math-container">$$m\ddot y=F_y+F_{cy}$$</span>
<span class="math-container">$$m\ddot z=F_z+F_{cz}$$... | 44 |
classical mechanics | The angular momentum and angular velocity roles in precession | https://physics.stackexchange.com/questions/602576/the-angular-momentum-and-angular-velocity-roles-in-precession | <p>I'm not sure I understand this topic so I would be happy if someone could clarify it for me:</p>
<p>Is precession (say, of a spinning top) generally speaking a change in the <strong>direction</strong> of the angular velocity vector over time? Is that why it is sometimes said that whenever <span class="math-container... | <p>If a symmetrical object is spinning with an angular velocity, ω, then the angular momentum, L = I ω (with both vectors along the axis of rotation). If an external torque (often from gravity) is applied, then the angular momentum vector (and the axis of rotation) swing in the direction of the torque vector: τ = dL/d... | 45 |
classical mechanics | Why don't we consider pressure as the driving agency for motion, instead of force, because the force applied is on an area/part of the body only? | https://physics.stackexchange.com/questions/603949/why-dont-we-consider-pressure-as-the-driving-agency-for-motion-instead-of-forc | <p>Because the force applied on a body obviously would act on a particular area, and not the whole body.</p>
| <p>Because it's a lot easier to work with. You could use pressure to calculate how an object will move/behave but you would have to work out the average pressure acting on the body and multiply it by the surface area which would give you the force anyway.</p>
<p>It is similar to how we model gravity to be acting on an ... | 46 |
classical mechanics | Is the total energy conserved in a moving reference frame? | https://physics.stackexchange.com/questions/4827/is-the-total-energy-conserved-in-a-moving-reference-frame | <p>I have a ball attached to a spring and the spring is attached to a wall. There is no gravity for simplicity. In the rest RF the oscillating ball energy is conserved: T + U = const. In a moving RF it is not conserved. I would like to see the shortest answer to the question "Why?".</p>
<p>| <-- --><br>
... | <p>Energy is <strong>not</strong> a Lorentz scalar (or Galilean scalar). In different reference frames, the values of energies wil also be different, but this does not mean that there is no energy conservation. The energy is still conserved in <strong>each</strong> reference frame.</p>
| 47 |
classical mechanics | Why does the net lift of an airship remain constant when the Kg of air it displaces should fall as altitude increases and pressure decreases? | https://physics.stackexchange.com/questions/583498/why-does-the-net-lift-of-an-airship-remain-constant-when-the-kg-of-air-it-displa | <p>In the paper, <a href="https://www.researchgate.net/publication/228609262_Development_of_an_Aerodynamic_Model_and_Control_Law_Design_for_a_High_Altitude_Airship_presented_at" rel="nofollow noreferrer">Development of an Aerodynamic Model and Control Law Design for a High Altitude Airship</a> I found a passage that ma... | <p>Bouyant force is given by</p>
<p><span class="math-container">$F_B = \rho Vg$</span></p>
<p>As the airship rises, the outside air pressure does decrease as well, meaning the helium in the airship expands (which means you are correct in that its density decreases for the same mass). Therefore, the amount of displaced... | 48 |
classical mechanics | Matching torque SI units from two different formula | https://physics.stackexchange.com/questions/587464/matching-torque-si-units-from-two-different-formula | <p>Torque = r x F = r*F*sin(theta) => So units will be kg*m^2/s^2</p>
<p>Torque = I*alpha => SI units is kg*m^2*rad/s^2</p>
<p>There is a rad unit extra in the second formula. They both should match right because they are calculating torque.</p>
| <p>Rad or radians has no physical dimensions and so both these equations are correct.</p>
| 49 |
classical mechanics | Non Classical mechanic answer to : length of time a thrown object spends in rest before falling down? | https://physics.stackexchange.com/questions/3372/non-classical-mechanic-answer-to-length-of-time-a-thrown-object-spends-in-rest | <p>When an object is thrown upwards, when it eventually comes to rest and starts falling, for how long is it stationary? What about an particle in electric field having an initial velocity towards it's same charge? That too would come to rest and reverse velocity, the question is for how long is it at full stop with re... | <p>Another result is <a href="http://en.wikipedia.org/wiki/Earnshaw%27s_theorem" rel="nofollow" title="Earnshaw's_theorem">Earnshaw's_theorem,</a> which tells us that no particle can ever be held in a stable equilibrium in the presense of any other collection of interacting particles.</p>
| 50 |
classical mechanics | max velocity of SHM | https://physics.stackexchange.com/questions/4189/max-velocity-of-shm | <p>So I think my algebra is wrong somewhere.
Lets say you have an object that goes under SHM with some initial conditions (amplitude is 5m. The piston is at 5m at t = 0 and period is 20 seconds).</p>
<p>Okay so $x(t) = A sin(\omega_0 + \phi)$. $\phi$ for us is 0. The frequency = $0.05 Hz$, angular frequency = $\frac{\... | <blockquote>
<p>But the value t = 20s represents the object at x = Amplitude.</p>
</blockquote>
<p>Check this calculation again. Remember your formula is $x(t) = A sin(\omega_0 t)$, and you should get full credit on your homework.</p>
<p>(or at least mostly full credit. There are many values of $t$ that satisfy $c... | 51 |
classical mechanics | Force on suspension when hitting a step | https://physics.stackexchange.com/questions/574523/force-on-suspension-when-hitting-a-step | <p>I'm trying to calculate the magnitude and direction of the force exerted on a wheel when encountering a step. The wheel and the steps are non-deformable.</p>
<p>I found two different approaches:</p>
<ul>
<li><p>energy approach, from which I can calculate the difference in speeds before and after, but I have no idea ... | <p>If you had a lone wheel of known size and mass which experiences no friction at the point of contact, you might be able to simulate this situation. The problem is that the force of contact changes in both magnitude and direction as the wheel rises up over the step.</p>
| 52 |
classical mechanics | Constaints in Rotation matrix | https://physics.stackexchange.com/questions/575225/constaints-in-rotation-matrix | <p>In Rigid body rotation, we need only 3 parameters to make a body rotate in any orientation. So to define a rotation matrix in 3d space we only need 3 parameters and we must have 6 constraint equation (6+3=9 no of elements in rotation matrix)</p>
<p>My doubt is if orthogonality conditions R.Transpose(R)=I must be sat... | 53 | |
classical mechanics | Torque when jumping from AT-REST Merry Go Round, Conservation of Angular momentum | https://physics.stackexchange.com/questions/577125/torque-when-jumping-from-at-rest-merry-go-round-conservation-of-angular-momentu | <p>Say there a child, that stands on the edge of an AT REST merry go round. When they jump off, the child has a linear velocity, and the merry go round begins to turns.</p>
<p>They say there is no net torque on the merry go round/child system and angular momentum is conserved.</p>
<p>I understand the torque applied to ... | <blockquote>
<p>I understand the torque applied to the merry go round from the child(force of child x radius of merry go round), but how does the merry go round provide a torque to the child. Doesn't it just apply a force?</p>
</blockquote>
<p>Torques are "just forces", but interpreted about a specific point ... | 54 |
classical mechanics | Angular velocity and rotation matrices | https://physics.stackexchange.com/questions/585208/angular-velocity-and-rotation-matrices | <p>I'm running into some confusion understanding rotations as being instantaneous cross products of angular velocity vectors. I would like to highlight two approaches which seem like they contradict each other, in the hopes that somebody can explain the conceptual error being made.</p>
<p><strong>Approach 1</strong></p... | 55 | |
classical mechanics | Is it possible that a satellite rotates planet infinitely without air resistance? | https://physics.stackexchange.com/questions/593615/is-it-possible-that-a-satellite-rotates-planet-infinitely-without-air-resistance | <p>I am ignorant of physics besides college, and I would like to know if it is possible that a moon rotates its mother planet for an infinite time assuming there is no resistance of any form.</p>
<p>I came up with this question since once a moon starts rotating, it keeps rotating according to law of gravity. Isolate th... | <p>In an isolated Kepler system, the orbits will continue indefinitely.</p>
<p>This is not a problem as regards the second law of thermodynamics, as no work is being extracted from the system. The entropy of the system is constant, consistently with the non-decreasing constraint.</p>
<p>(In the real world, of course, t... | 56 |
classical mechanics | Are all kinds on Forces between particles only dependent on the distance between the particles? | https://physics.stackexchange.com/questions/535953/are-all-kinds-on-forces-between-particles-only-dependent-on-the-distance-between | <p>The 'total energy' of a particle in an isolated system is conserved only if all the forces on it are conservative. For a conservative force, we need a force dependent only on the current position of the particle, right? Is every force in the universe like that? Coloumb and Gravitation Forces are like that, and I thi... | <p>No, not all of them, actualy most of them do not. Coulomb and Gravitational Newton force have such simple form because they describe interaction between particles at rest (unmoving) and with no other qualities that scalar electric charge and mass. The situation they are supposed to describe is so simple there isn't ... | 57 |
classical mechanics | What happens if a particle moving in a hollow sphere is given a horizontal velocity | https://physics.stackexchange.com/questions/536095/what-happens-if-a-particle-moving-in-a-hollow-sphere-is-given-a-horizontal-veloc | <p>Consider a heavy particle moves inside a frictionless hollow sphere with radius a.<br>
The particle is
held on the inner surface of the sphere at z = −a/2, where z is measured upwards from the centre of the sphere. Given a horizontal velocity U. If U squared = 4ag,
find the maximum and minimum height that the parti... | 58 | |
classical mechanics | Free falling bodies: why air resistance is not considered? | https://physics.stackexchange.com/questions/536270/free-falling-bodies-why-air-resistance-is-not-considered | <p>We affirm that free falling bodies are by definition bodies that are subject to the sole force of gravity. We state that free falling bodies fall through equal distances in equal times regardless their different weight. Most of the experiments that show this evidence are executed in normal conditions here on earth; ... | <blockquote>
<p>we see that dropping a bowling ball and a ping-pong ball, the two objects touch the ground at the same moment despite their different weight.</p>
</blockquote>
<p>Not when I do the experiment. In fact Galileo had a hard time convincing his colleagues that, without air resistance, they would fall at t... | 59 |
classical mechanics | Shooting a moving target from a moving target? | https://physics.stackexchange.com/questions/536716/shooting-a-moving-target-from-a-moving-target | <p>What is the physics of shooting a moving target from a moving target? Bullet turns, target moves, and one have to pre-aim to compensate the difference such as World War II fighter plane. Does it even have a name?</p>
| <p>Shooting at a moving target, whether or not you are moving, is known as deflection shooting. There is no special name just because the gun platform is also moving.</p>
<p>Besides the obvious things like relative motion, distance and the time of flight of the projectile, you need to know many other things. The attit... | 60 |
classical mechanics | Is a free particle one on which there's no NET force or one on which there's no force at all? | https://physics.stackexchange.com/questions/537933/is-a-free-particle-one-on-which-theres-no-net-force-or-one-on-which-theres-no | <p>I'm getting different definitions from different sources. Some claim that free particles have no forces acting on them at all (i.e. even if a particle has forces acting on it such that they cancel, it's not free). Other sources explicitly state that there is no net force (like <a href="https://www.tau.ac.il/~tsirel/... | <p>Forces often come from force fields like gravitational or electromagnetic. These differ in different parts of space, so they may cancel in one point but not in another.</p>
<p>Now, suppose a particle is at a point where all forces cancel (and there's a non-empty set of forces being in superposition). Let's now pert... | 61 |
classical mechanics | What are the fields in this problem? | https://physics.stackexchange.com/questions/41925/what-are-the-fields-in-this-problem | <p>In problem 3 of chapter 2 of Landau Lifshitz "Mechanics," I don't understand the meaning of the fields as defined in the following statement:</p>
<blockquote>
<p>Which components of momentum and angular momentum are conserved in motion in the following fields?</p>
<p>(a) the field of an infinite homogeneou... | <p>Yes, that is what Landau and Lify are getting at. I don't really see another interpretation. I mean, are momentum and angular momentum conserved under the following applied potential fields? I think that is a reasonable interpretation. Haven't looked at Landau and co. Mechanics in a bit, but this seems reasonable. <... | 62 |
classical mechanics | Spiral path of particle moving under circular force | https://physics.stackexchange.com/questions/565672/spiral-path-of-particle-moving-under-circular-force | <p>Imagine a situation where a long masless stick is inserted through a ring, and fix one of the ends of the stick. Then, the system is given an impulsive force such that it starts rotating with an initial velocity <span class="math-container">$\omega_0$</span>, the ring will start moving outwards, and thus, the system... | <p><strong>Hint:</strong>
You can write <span class="math-container">$\omega= \dot{\theta}$</span>, and cancel the <span class="math-container">$dt$</span> in the second equation, so it becomes seperable in <span class="math-container">$r$</span> and <span class="math-container">$\omega$</span>.</p>
| 63 |
classical mechanics | Are forces from different directions applied to a hanging mass the same? | https://physics.stackexchange.com/questions/565901/are-forces-from-different-directions-applied-to-a-hanging-mass-the-same | <p>Let's assume a mass that is hanging somewhere. My question is basically:</p>
<ol>
<li>We are applying a force from the side to move the mass sidewards</li>
<li>We are applying a force from below to move the mass upwards</li>
</ol>
<p>Are these forces the same?</p>
<p>In this context, a bit more concise and realistic... | <p>Yes, because the mass <span class="math-container">$m$</span> is a scalar quantity and when you describe Newton's 2nd law in vector form you have</p>
<p><span class="math-container">$$ \vec{F} = m\, \vec{a}$$</span></p>
<p><span class="math-container">$$ \pmatrix{F_x \\ F_y} = m \pmatrix{a_x \\ a_y} = \pmatrix{m\, a... | 64 |
classical mechanics | Disintegration of many particles Landau (Mechanics 3rd Ed page $43$) | https://physics.stackexchange.com/questions/571565/disintegration-of-many-particles-landau-mechanics-3rd-ed-page-43 | <p>On page <span class="math-container">$41$</span> Landau states that the total momentum in the C system is <span class="math-container">$0$</span>.</p>
<p>On page <span class="math-container">$43$</span> for the disintegration of many particles, Landau states: In the C system... every resulting particle (of a given k... | 65 | |
classical mechanics | horizontal motion inside a cone (cylindrical polars) | https://physics.stackexchange.com/questions/104836/horizontal-motion-inside-a-cone-cylindrical-polars | <p>I have a question from an example we done in lecture</p>
<p>Suppose we have a particle moving inside the surface of a cone given by $r = wz$ where $w$ is a constant,</p>
<p>and also suppose initially the particle is moving horizontally at height $b$ and speed $U$,the lecturer then stated these "facts"</p>
<p>$\un... | <p>It says "<em>initially</em>, $\dot r = \dot z = 0$". This is synonymous with $\dot r(0) = \dot z(0) = 0$. Vague wording like that is usually to trick students.</p>
| 66 |
classical mechanics | How to reconcile angular momentum measurements? | https://physics.stackexchange.com/questions/109211/how-to-reconcile-angular-momentum-measurements | <p>Imagine a particle tracing a counter-clockwise circular path on a flat table with a certain speed. The particle is tied with a massless string of length $R$ to a point $P$ at the center of the circular path. Will the particle rotate about $P$ forever at constant speed in the absence of any external force? Consider u... | <p>Your error lies in your last paragraph:</p>
<blockquote>
<p>Because the angular momentum $\vec{L}'$ is not conserved due to changing direction, and a changing $\vec{L}'$ requires the presence of an external force to give rise to a net torque $\vec{\tau}'$ about the point that is used to measure $\vec{L}'$, which ... | 67 |
classical mechanics | Two-Body with external force - energy confusion | https://physics.stackexchange.com/questions/109239/two-body-with-external-force-energy-confusion | <p><strong>Setup</strong></p>
<p>Imagine a two-body system of masses under a classical mechanics model. The separation and mass-ratio doesn't matter for this example. Presume they are initially stationary.</p>
<p>Now suppose that we hold one of the masses, m1, permanently stationary with an external force opposing th... | <p>The system of the two masses does not experience work due to the external force. You are using the wrong displacement. You should use the displacement of the "point of application" of the external force to calculate work for a given force, even if that force is applied to some system. In particular, don't use the ce... | 68 |
classical mechanics | upwind vehicle exceeding the wind speed | https://physics.stackexchange.com/questions/110395/upwind-vehicle-exceeding-the-wind-speed | <p>Has anyone done any research about the upwind vehicle <a href="http://www.popsci.com/cars/article/2012-07/wind-powered-car-travels-upwind-twice-speed-wind" rel="nofollow">http://www.popsci.com/cars/article/2012-07/wind-powered-car-travels-upwind-twice-speed-wind</a>?</p>
<p>I think it is impossible but get a surpri... | <p>There no hard theoretical upper limit on the true wind multiple a wind-powered vehicle can achieve. It's just a matter of practically achievable efficiency. This applies to all directions, including directly upwind and directly downwind.</p>
<p>The mechanical principle can be demonstrated with a simple gear-toy, wh... | 69 |
classical mechanics | How was it possible to beat a soldier with a full plate armor? | https://physics.stackexchange.com/questions/113124/how-was-it-possible-to-beat-a-soldier-with-a-full-plate-armor | <p>From my point of view, it seems that a soldier armed with a <strong>full metal plate armor</strong> was almost invulnerable at the time their opponents yielded swords, spears or bows. I understand that it couldn't be the case, but I'm not sure about the physics behind it.</p>
<p>More specifically:</p>
<ol>
<li><p>... | <p>A crossbow would easily penetrate the armor. The bolt has more kinetic energy than a 45 magnum. </p>
<p>Long bows might penetrate the armor, especially the thinner areas. </p>
<p>Wielding a sword is tiring. Most people would need to rest after 15 minutes, warriors might go 30 minutes before needing to rest. When y... | 70 |
classical mechanics | Does lever needs gravitation to work? | https://physics.stackexchange.com/questions/131044/does-lever-needs-gravitation-to-work | <p>Simple question - Does lever needs gravitation force to work or it just needs fulcrum and could work in vacuum as well?</p>
| <p>A lever can work in zero-gravity conditions as long as the fulcrum and lever arm are physically attached. They also work regardless of atmospheric presence.</p>
| 71 |
classical mechanics | Which way to lean when driving a gokart? | https://physics.stackexchange.com/questions/132476/which-way-to-lean-when-driving-a-gokart | <p>Given a car that has two lines of wheels, the center of gravity at constant height above the ground, constant turn angle and given surface and wheel material.</p>
<p>What is the maximum speed the car can drive without the wheels sliding given the position of center of gravity (leaning in, leaning out or central)?</... | <p>I believe the correct approach in a go-kart is leaning outwards.
I think this is useful because go-karts do not have a differential between the left and right wheels. So the wheels are forced to turn at the same rate. Because the turn radius is not the same for the inner and outer wheels there must be some slip. Lea... | 72 |
classical mechanics | Concept map/graph | https://physics.stackexchange.com/questions/134046/concept-map-graph | <p>Where can I find maps of physical concepts illustrating the connection & logical relations between concepts . I think it can be of a great help to summarize what I learnt . </p>
| 73 | |
classical mechanics | How to calculate when an object will fall over | https://physics.stackexchange.com/questions/150582/how-to-calculate-when-an-object-will-fall-over | <p>TL;DR Given the point of centre of mass, width of base and height, is there a way to calculate the angle where the object will fall over?</p>
<p>The TL;DR of this question pretty much sums it up, however I wanted to give an example.</p>
<p>Let us say that we have a cuboid made of uniform weight wood with the dimen... | <p>The answer is actually more simple that you think. The tipping point is reached when the x coordinate of the center of mass is the same as the horizontal position of the last contact point. In the case of your cube there is only a contact point. But for instance, if you had a trapezoid at a table, it would tip if th... | 74 |
classical mechanics | How do I turn my bicycle? | https://physics.stackexchange.com/questions/156197/how-do-i-turn-my-bicycle | <p>No doubt a very simple question with an easy answer that's been puzzling me:</p>
<p>If I'm riding my bicycle in the $x$ direction with speed $v$ and turn my handlebars I can end up travelling in the $y$ direction with almost the same speed without having to provide any additional energy. I don't have to come to a h... | <p>Actually unless you lean over you will tip when you turn the wheel. It is the leaning that changes the direction of travel and the handlebars only provide fine tuning of the motion.</p>
<p>The component of gravity perpendicular to the plane of the bike provides for a force that does no work (since its perpendicular... | 75 |
classical mechanics | Taking moments about two different points in a system of forces | https://physics.stackexchange.com/questions/165074/taking-moments-about-two-different-points-in-a-system-of-forces | <p>If you have a system of forces and you take moments about two different points will the moment be the same?</p>
| <p>No. You can see now why dealing with torques and angular momentum is so difficult: It depends on what point in space you are taking it with respect to. The torque about one point may be different in both magnitude and direction of another arbitrary point. </p>
<p>If you are dealing with a system in static equilibri... | 76 |
classical mechanics | Are launch angles relative to observers? | https://physics.stackexchange.com/questions/171988/are-launch-angles-relative-to-observers | <p>Supposed we have someone on a moving platform which is at constant velocity. Lets say the person launches a mass at some speed relative to the platform an some angle with respect to the platform. Does the launch angle differs from say someone on the ground? </p>
<p>I know velocities are relatives, but I really can'... | <p>The angle between the object being launched and the platform from which it is launched should remain the same to all observers unless they are moving at speeds comparable to the speed of light relative to the platform. At these speeds they will observe length contraction, the length along the axis which the objects ... | 77 |
classical mechanics | Definition of kinetic energy without the second Law of Newton | https://physics.stackexchange.com/questions/176436/definition-of-kinetic-energy-without-the-second-law-of-newton | <p>As I see it, the definition of kinetic energy
$$T= {1\over2} m u^2 \text { where $u<<c$}$$
comes by using the definition of work
$$W= {\int F\cdot\ dx }$$
and we use for the meaning of F(force) the Second Law of Newton:
$$F={dp\over dt}=ma$$</p>
<p>Do I understand correctly that the kinetic energy from th... | <p>You can define the kinetic energy as you want. As long as they are consistent with each other, definitions are yours to choose.</p>
<p>For example you can take
$$T = \frac{1}{2}m v^2 \, ,$$
as a definition and use it to <strong>prove</strong> Newton's law by requiring energy to be conserved,
$$ \frac{dE}{dt} = \fra... | 78 |
classical mechanics | name of this bouncing balls separator model | https://physics.stackexchange.com/questions/184308/name-of-this-bouncing-balls-separator-model | <p><a href="https://www.youtube.com/watch?v=SRGf0Mq2Zwg" rel="nofollow">https://www.youtube.com/watch?v=SRGf0Mq2Zwg</a></p>
<p>I want to read the physical and mathematical model of this "bouncing balls separator " in the above link .</p>
<p>What is name of this experiment so I can search it in literature ?</p>
| 79 | |
classical mechanics | What are possible explanations for the permeability of balloon rubber, PET plastic and other synthetic materials for carbon dioxide? | https://physics.stackexchange.com/questions/187868/what-are-possible-explanations-for-the-permeability-of-balloon-rubber-pet-plast | <p>Balloons are definitely not gas-tight. Carbon dioxide just leak by the rubber away. A balloon is filled with carbon dioxide. Knot in it. And play. Shrinkage. After an hour or two the carbon dioxide balloon has dramatically shrunk in size. Apparently carbon dioxide creeps much faster through the rubber balloon than ... | 80 | |
classical mechanics | Proof of vertical and horizontal velocity component in projectile motion | https://physics.stackexchange.com/questions/191201/proof-of-vertical-and-horizontal-velocity-component-in-projectile-motion | <p>Why is it that $v\cdot sin(x)$ gives the vertical component and $v \cdot cos(x)$ gives the horizontal component, where $v$ is the speed? What logic is there behind it, or even better is there a proof to back it up?</p>
<p>I know by drawing a right angled triangle you can find out the components, but I want a deeper... | <p>Tl;dr: Vector components act like sides of a triangle, where the length of the vector coincides with the triangle's hypotenuse.</p>
<hr>
<p>Mathematically, this follows from the fact that velocity in the plane is an element $v \in \mathbb{R}^2$. Consider a Euclidean coordinate system whose origin coincides with th... | 81 |
classical mechanics | Why is a bending rod assumed to be undergoing torsion? | https://physics.stackexchange.com/questions/188334/why-is-a-bending-rod-assumed-to-be-undergoing-torsion | <p>If I take a rod and bend it at both ends as far as it will go, why is there an assumption that I am also exerting a torsion along with my bending?</p>
<p>Referencee: ccording to the third edition of "Theory of Elasticity": </p>
<blockquote>
<p>"It is important to note that, when a rod undergoes larding
deflect... | <p>Without further context I believe what the book is saying is that when one applies a pure bending moment stress in a beam that the resulting strain is not nessiarily purely in bending, but will also include torsional strain.</p>
<p>For example, if one looks purely at bending moments and assumes that no torsional st... | 82 |
classical mechanics | How does rotational energy transfer to linear energy? | https://physics.stackexchange.com/questions/196946/how-does-rotational-energy-transfer-to-linear-energy | <p>So I have recently started looking into moments of inertia, and all that stuff. I have come to a question which has a plane inclined at some angle theta and a sphere at the peak. The G.P.E at the top is mgh. The plane is frictionless.The book then states by conservation of energy $mgh = 1/2(mv^2) + \text{rotational ... | <blockquote>
<p>Firstly I don't understand how if the ball is initially rotating how it gains rotational energy from the top of the plane to the bottom, since there is no friction to provide torque. </p>
</blockquote>
<p>Your understanding is mostly correct. We can choose any point on the object to measure rotation ... | 83 |
classical mechanics | spin-orbit coupling for a rigid body | https://physics.stackexchange.com/questions/200574/spin-orbit-coupling-for-a-rigid-body | <p>Consider the motion of a coffee cup in the gravitation field of earth. The force acting on the cup apparently depends on the orientation of the cup. Therefore, the internal rotation (with respect to its center of mass) of the cup is coupled with its center-of-mass motion. Is this a classical counterpart of the spin-... | 84 | |
classical mechanics | A metal block in a tub of frictionless ball bearings | https://physics.stackexchange.com/questions/197187/a-metal-block-in-a-tub-of-frictionless-ball-bearings | <p>If you place a metal block in a tub of small frictionless ball bearings of the same metal, would it stay on top or sink?..</p>
| <p>The block will have higher density because of the air gaps between the steel balls so it should sink to the bottom.</p>
| 85 |
classical mechanics | Limits of integration | https://physics.stackexchange.com/questions/200830/limits-of-integration | <p>In the following video can someone explain why did he take the limits of integration to be from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ ?
<a href="https://www.youtube.com/watch?v=bJWFgJTxIFk&index=9&list=PLYVDsiuOZP5pNzoB-e4ugTz96dGpspdDI" rel="nofollow">https://www.youtube.com/watch?v=bJWFgJTxIFk&index=9&a... | <p>The person in the video took $\theta$ to be from the vertical axis. This was stated in the video itself.</p>
<p>You might be more familiar with taking an angle to measure going counter-clockwise from the 3 o'clock position. If you want to measure angles that way then you can go from $0$ to $\pi$ and this was explai... | 86 |
classical mechanics | Hausdorff spaces and finite elements | https://physics.stackexchange.com/questions/202505/hausdorff-spaces-and-finite-elements | <p>Must the shape functions and the interpolation functions (which are the same in an isoparametric element) in a finite element model be elements of a Hausdorff space? If so, is this necessary to ensure convergence to a unique solution when the mesh is refined? If not, what are the requirements for these functions... | 87 | |
classical mechanics | Why must an inertial navigation system take the Coriolis effect into account? | https://physics.stackexchange.com/questions/205126/why-must-an-inertial-navigation-system-take-the-coriolis-effect-into-account | <p>I read somewhere that an inertial navigation system, in order to be accurate, must take the Coriolis effect into account. Why is this so? If I go a 500 mph velocity in a given direction, I'm going 500 mph, so in 1 hour, I should be 500 miles from the airport whether I'm traveling N, E, or W. </p>
| <p>To a stationary observer on Earth watching you travel in the same direction in which the Earth rotates, you might be going 500 mph. Galilean relativity says that you are moving 500 mph relative to Earth, and the Earth is moving 500 mph relative to you.However, since the Earth is rotating, that stationary observer is... | 88 |
classical mechanics | A system of particles interacting via conservative forces, will also respect $U_2+K_2=U_1+K_1$ | https://physics.stackexchange.com/questions/205145/a-system-of-particles-interacting-via-conservative-forces-will-also-respect-u | <p>Studying vector calculus you learn to prove that a particle moving in a gravitational field will, in that field respect that $dU=-dW$. From this you can conclude $U_2+K_2=U_1+K_1$. </p>
<p>This is easy to prove in here but I fail to see how to prove it for, suppose, $n$ charged particles or massive particles.</p>
... | <p>A force is conservative iff there exists a potential $\Phi$ such that ${\bf F} = -\nabla\Phi$. The Lagrangian for a system of $n$ particles acting under (any number of) conservative forces can be written on the general form</p>
<p>$$L = \sum_{i=1}^n \frac{1}{2}m_i{\bf \dot{r_i}}^2 - \Phi({\bf r_1},{\bf r_2},\ldots,... | 89 |
classical mechanics | Can we change the rotation speed of Earth if all cars, planes, ships, etc travel towards east or west together? | https://physics.stackexchange.com/questions/207444/can-we-change-the-rotation-speed-of-earth-if-all-cars-planes-ships-etc-travel | <p>I know when cars drive, there is action and reaction pair on the wheel, then is it possible to speed up or slow down the rotation of Earth if all cars and other machines travel towards one direction together?</p>
| <p>Earth + machines is an isolated system so angular momentum is conserved
\begin{align}
I_{\text{Earth}}\omega_{\text{Earth}}^{\text{before}} &= I_{\text{Machine}}\omega_{\text{Machine}} + I_{\text{Earth}}\omega_{\text{Earth}}^{\text{after}}\\
\Rightarrow
&\frac{\omega_{\text{Earth}}^{\text{after}}}{\omega_{\t... | 90 |
classical mechanics | How physics opens a knife with a flick of the wrist? | https://physics.stackexchange.com/questions/212150/how-physics-opens-a-knife-with-a-flick-of-the-wrist | <p>A person holds the handle of a folding knife in their hand with the pivot point of the blade between their index finger and thumb. The blade points away from the body and the other fingers grip the handle in a way not to impede the opening of the blade. The friction at the pivot point is just enough for the blade to... | <p>Think of the example of a passenger in a car. When the car is moving in uniform motion (acceleration = 0) the passenger is not moving relative to the car. However if the car slows down or speeds up, the passenger begin to resist the motion of the car (i.e. car slows down passenger moves forward relative to the car).... | 91 |
classical mechanics | Rotating disc problem | https://physics.stackexchange.com/questions/218166/rotating-disc-problem | <p>This question comes into my mind this evening. </p>
<p>Suppose I have a rotating disc whose maximum rotation speed is $500$ rpm (say). On this rotating disc I have placed another small rotating disc with same property and in such a way that both can rotate in this configuration. Now if I started the disc below, it ... | <p>If they rotate in the same direction at the same speed, there will be no effect. This is because the disks do not move relative to one another.</p>
<p>If they rotate at different speeds or in different directions and there is friction between the disks, their speeds will gradually come closer to one another's until... | 92 |
classical mechanics | Probability of light being refracted in deep space by H 2(Hydrogen) | https://physics.stackexchange.com/questions/228538/probability-of-light-being-refracted-in-deep-space-by-h-2hydrogen | <p>Is it a valid question to ask what is the percentage of light that gets refracted by H 2 for a certain distance(Lets say 1 light year) in deep space. Lets assume a few(3) Hydrogen atoms per cubic meter. </p>
| 93 | |
classical mechanics | When an object is moving at a constant velocity,would the normal force and $mg$ be equal? | https://physics.stackexchange.com/questions/228701/when-an-object-is-moving-at-a-constant-velocity-would-the-normal-force-and-mg | <p>Does the object's normal force and $mg$ cancel out, resulting in the two force becoming equal, or would one force be greater than the other? Thank you!
Edit: Also would the $mg$ be considered weight or would it be more correct to just refer to the force as $mg$? </p>
| <p>If the object is moving on a horizontal frictionless surface, then the normal force equals $mg$.</p>
<p>Yes, $mg$ is the weight of the object.</p>
| 94 |
classical mechanics | Detached wheel from a moving vehicle speed | https://physics.stackexchange.com/questions/228301/detached-wheel-from-a-moving-vehicle-speed | <p>If a wheel is detached from a moving vehicle, would it speed be higher than the vehicle? Why?</p>
| <p>Assume the car travels at speed $v$ and the wheel has a radius $R$. Assume also that the wheel was rolling without slipping, then:</p>
<p>$$v=\omega R,$$</p>
<p>where $\omega$ is the <em>angular speed</em> of the wheel.</p>
<p>When the wheel detaches from the car and assuming no torques or forces act on it from t... | 95 |
classical mechanics | How am I able to keep my footing on an accelerating platform? | https://physics.stackexchange.com/questions/226483/how-am-i-able-to-keep-my-footing-on-an-accelerating-platform | <p>When I'm standing in a train car and the train starts slowing down relatively quickly, I instinctively flex certain muscles in my legs and that helps me keep my footing. </p>
<p>What muscles am I flexing and how does flexing them help me maintain my balance and avoid falling?</p>
| <p>I'll answer this as a physics question. To avoid falling over, you need to keep your center of gravity "over" your feet, where "over" means that the vector sum of gravitational and train acceleration points from your $CG$ down to between your feet. To do this, you lean towards the front of the train so as to move yo... | 96 |
classical mechanics | Kinetics of gas molecule | https://physics.stackexchange.com/questions/231889/kinetics-of-gas-molecule | <p>In the explanation of the nature of gases we use the kinetic formula $PV=1/3(mnc)$
where $p$ is pressure, $v$ volume, $m$ mass, $n$ number of molecules and $c$ means root mean square velocity. But in its explanation I don't understand why everyone uses time to measure the change of momentum of a particular molecule,... | 97 | |
classical mechanics | If a bullet penetrates a bag, how come the repulsive force is constant? | https://physics.stackexchange.com/questions/232326/if-a-bullet-penetrates-a-bag-how-come-the-repulsive-force-is-constant | <p>I was doing a question on energy and forces, and it goes as follows:(Doesn't require knowledge of calculus):</p>
<blockquote>
<p>If a bullet with velocity $v$ penetrates a bag upto a distance $x$,
then find the distance which bullet penetrates if velocity becomes
$2v$.</p>
</blockquote>
<p>I tried to solve i... | <p>The force is most likely not constant but your teacher wanted you to be able to do the problem in not too long a period of time.</p>
| 98 |
classical mechanics | Can point mass have vibrational motion? | https://physics.stackexchange.com/questions/234561/can-point-mass-have-vibrational-motion | <p>Can a point mass have vibrational motion. I have read that reason for point mass is to ensure that we can idealize translational motion and don't have to worry about rotational and vibrational motion. Is that correct?</p>
| <p>It depends what you mean by vibrational motion. A point mass indeed does not have <em>internal</em> vibrational degrees of freedom, it can just have translational motion, as you pointed out.</p>
<p>However, if you attach this point mass to a spring you create a harmonic oscillator. It has a translational motion, bu... | 99 |
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