Physics Problems Q&A - Recent questions in Physics Problems
http://physics.qandaexchange.com/?qa=questions/physics-problems
Powered by Question2Answergraphing height and speed of projectiles
http://physics.qandaexchange.com/?qa=3485/graphing-height-and-speed-of-projectiles
<p>The football ball m=1kg was kicked up vertically with speed v=30m/s. Make the model of<br>
movement track, also the graph of speed, knowing that Fr=bv2</p>
<p>, b=1 N/m2<br>
.</p>
<ol>
<li>The football ball m=1kg was kicked up vertically with speed v=20m/s. Make the graph of speed<br>
and the y position.</li>
<li>The stone was thrown horizontally with speech v=10m/s, from the building at high h=15m.<br>
Make the model of movement track, also the graph of speed.</li>
<li>The mass m1=1 kg is moving on inclined plane, inclined with an angle θ=30°. Kinetics friction<br>
coefficient μk=0.2. Make the graph of speed and the movement.</li>
</ol>
Physics Problemshttp://physics.qandaexchange.com/?qa=3485/graphing-height-and-speed-of-projectilesWed, 19 Jun 2019 11:05:15 +0000Current through a particular branch of RC circuits
http://physics.qandaexchange.com/?qa=3474/current-through-a-particular-branch-of-rc-circuits
<p><img src="https://imgur.com/SMy8Cdb.png" alt=""></p>
<p>I'm done with part A, B and C, please help me to find the current through the resistor if I can calculate the current through $1.2M$ ohm then using Kirchoff's laws we can do part D, but I don't know how, please help.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3474/current-through-a-particular-branch-of-rc-circuitsSat, 18 May 2019 15:23:31 +0000How to use symmetry?
http://physics.qandaexchange.com/?qa=3473/how-to-use-symmetry
<blockquote><p>For the following circuit find the current through $6$ ohm and $3$ ohm.<br>
<img src="https://imgur.com/su538rl.png" alt=""></p>
</blockquote>
<p>I can solve with other method but please help me to know how to use symmetry methods to solve this.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3473/how-to-use-symmetrySat, 18 May 2019 14:08:28 +0000The photocurrent in the detector assuming all rays to be paraxial w.r.t. lens
http://physics.qandaexchange.com/?qa=3472/the-photocurrent-the-detector-assuming-rays-paraxial-lens
<p>A disc shaped photoelectric detector of area 0.5 $cm^2$ generates current when light of frequency > that of yellow light falls on it. The photoelectron generation efficiency is 20%. In the arrangement shown, S is an isotropic 100 watt point monochromatic light source with $\lambda$ =4000 A. The focal of the lens is 20 cm and its circular area is 4 $cm^2$. Find the photocurrent in the detector assuming all rays to be paraxial w.r.t. lens.<br>
<img src="https://i.imgur.com/BLHEHvY.png" alt=""></p>
<p>My try :</p>
<p><img src="https://i.imgur.com/FKHAEoD.jpg" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3472/the-photocurrent-the-detector-assuming-rays-paraxial-lensSat, 18 May 2019 02:33:26 +0000Net energy loss in infinite series of capacitors
http://physics.qandaexchange.com/?qa=3460/net-energy-loss-in-infinite-series-of-capacitors
<p><img src="https://imgur.com/PqsK79D.png" alt=""></p>
<p>Here $Q=4\pi \epsilon_0 RV$ and $ C=4\pi \epsilon_0 R$</p>
<p>While solving i got the energy loss when S2 is closed as $$E_i-E_f = \frac{Q^2}{2C} - (\frac{Q^2}{8C} + \frac{Q^2}{8C})$$<br>
since $Q$ on 1st capacitor equally divides between 1st and 2nd capacitor.</p>
<p>So energy loss when S2 is closed is $\frac{Q^2}{4C}$ and that when S3 is closed is $\frac{Q^2}{16C}$ and so on.</p>
<p>When I take the sum I get $\frac43\pi\epsilon_0 RV^2$ but that's not the answer.</p>
<p>What went wrong?</p>
<p><a rel="nofollow" href="https://imgur.com/PqsK79D">https://imgur.com/PqsK79D</a></p>
<p><img src="https://imgur.com/PqsK79D" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3460/net-energy-loss-in-infinite-series-of-capacitorsThu, 16 May 2019 14:31:42 +0000Velocity wrt COM
http://physics.qandaexchange.com/?qa=3465/velocity-wrt-com
<p>For problem: <a rel="nofollow" href="https://pasteboard.co/IeXpnsn.png">https://pasteboard.co/IeXpnsn.png</a>, find velocity with which small mass collide with bigger mass, on its return journey.<br>
<img src="https://i.imgur.com/CQ1dM9x.png" alt=""><br>
The solution given as <a rel="nofollow" href="https://pasteboard.co/IeXqMzD.png">https://pasteboard.co/IeXqMzD.png</a>, I don't understand why wrt Com small sphere will return with same but opposite directed velocity, please explain.<br>
<img src="https://imgur.com/BcqvGIf.png" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3465/velocity-wrt-comThu, 16 May 2019 11:44:38 +0000Find the equation of wave
http://physics.qandaexchange.com/?qa=3461/find-the-equation-of-wave
<blockquote><p>The linear mass density of a nonuniform wire under constant tension decreases gradually along the wire so that an incident wave is transmitted without reflection. The wire is uniform for $-\infty < x < 0$. In this region, a transverse wave has the form $$y(x, t) = 0.003 \cos (25x — 50t)$$ where $y$ and $x$ are in meters and $t$ is in seconds. In the region $0 < x < 20$ the linéar mass density decreases gradually from $\mu$ to $\frac14 \mu$. For $20 < x < +\infty$ the linear mass density is $\frac14 \mu$. Then prove that for $x > 20$ the wave equation is $$ y(x,t) = 0.0042 \cos (12.5 x — 50 t)$$</p>
</blockquote>
<p><img src="https://i.imgur.com/FkvLXz0.jpg" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3461/find-the-equation-of-waveWed, 15 May 2019 02:23:13 +0000Electric field for volume charge distributed slab
http://physics.qandaexchange.com/?qa=3455/electric-field-for-volume-charge-distributed-slab
<blockquote><p>A volume charge density given by $\rho(x,y,z) = \rho_0(z/a)$ forms a slab between the planes z=+a and z=-a . Outside the plates the charge density is zero . Calculate the electric field at points where z=0 and also where |z| <a.</p>
</blockquote>
<p>I wanted the potential but that turns out to be zero. How do I calculate the field by direct integration? </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3455/electric-field-for-volume-charge-distributed-slabSun, 12 May 2019 09:15:24 +0000To solve the equations of motion of a simple Pendulum $\ddot \theta = -\dfrac gl \sin \theta$
http://physics.qandaexchange.com/?qa=3454/solve-equations-motion-simple-pendulum-theta-dfrac-theta%24
<p>Hello,<br>
<img src="https://i.stack.imgur.com/j99Rs.jpg" alt="Pendulum"></p>
<p>I've a problem to calculate the Position of a pendulum as a function of theta.<br>
For example: $\theta (t)$ is a function of time which returns the angle made by the pendulum at a particular instant wrt it's equilibrium Position.</p>
<p>So, <br>
$$<br>
T = \dfrac 12 m l^2 \dot \theta^2 <br>
$$$$<br>
U = - mgl \cos \theta<br>
$$<br>
$$<br>
L(\theta, \dot \theta) = \dfrac 12 m l^2 \dot \theta^2 + mgl \cos \theta<br>
$$<br>
Using, the Euler - Lagrangian Formula, <br>
$$<br>
\dfrac d{dt} \left ( \dfrac{\partial L}{\partial \dot \theta}\right) - \dfrac{\partial L}{\partial \theta} = 0 <br>
$$<br>
We get, </p>
<p>$$<br>
\boxed{\ddot \theta =- \dfrac gl \sin \theta}<br>
$$<br>
which is the equation of motion.<br>
But, most of the derivations, I've seen/read go this way:<br>
$$<br>
\ddot \theta = \dfrac gl \theta \quad \dots \quad (\text{As, } \sin \theta \approx \theta, \theta \rightarrow 0) \tag{*}<br>
$$</p>
<p>$$<br>
\theta (t) = \cos \left ( \sqrt{\dfrac gl} t \right)<br>
$$<br>
Because it satisfies $(*)$</p>
<p>So, I've 2 questions here.</p>
<blockquote><ol>
<li><p>Other possible solutions of the Second Order Differential Equations exist like $\theta (t) = e^{\left( \sqrt{\dfrac gl}t \right)}$. So,<br>
why we choose that only one? One would argue that the sine function<br>
oscillates similar to the pendulum, so this makes sense to accept the<br>
sine one. But, in general case, when we solve the Lagrangian and get<br>
the equation of motion in differential form, then there are tons of<br>
complex situation possible, How can you determine which kind is<br>
needed?</p>
</li>
<li><p>How can we solve the Second Order Differential Equation $\ddot \theta = - \dfrac gl \sin \theta$ and get an exact formula for that?</p>
</li>
</ol>
</blockquote>
<p>Thanks :)</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3454/solve-equations-motion-simple-pendulum-theta-dfrac-theta%24Sat, 11 May 2019 02:38:32 +0000Thermal stress in a bar.
http://physics.qandaexchange.com/?qa=3450/thermal-stress-in-a-bar
<blockquote><p>Suppose a bar of length $L$, Young Modulus $Y$, temperature coefficient $\alpha$ is at temperature $T_o$ is just held between two walls. Now temperature increases, to make a change in temperature $\triangle T$ (measured from initial $T_o$). My book says thermal stress developed is $Y\alpha\triangle T$.</p>
</blockquote>
<p>My question:</p>
<p>As the rod is rigidly held, walls will not let rod to changes its length further from $L$, for this it applies force $F$. Its original length at $T_o+\triangle T$ would have been $L(1+\alpha\triangle T)$, if walls were not present, hence it causes $\triangle L=l\alpha\triangle T$.</p>
<p>So $Y=\dfrac{F_{T_f}\cdot L_{T_f}}{A\cdot\triangle L}\tag*{1}$ where $T_f$ signifies their respective values at final temperature. Putting these it gives to me themal stress as, $$\sigma=\dfrac{Y\alpha\triangle T}{1+\alpha\triangle T} $$.</p>
<p>If I were to put $L_{T_f}=L$ then this gives what my book says, but we should apply $\text{eq. 1}$ and put everything at the same temperature, so why putting its length as $L$ mandatory. Please help.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3450/thermal-stress-in-a-barFri, 19 Apr 2019 14:25:06 +0000time required to pass electricity through electroplating bath
http://physics.qandaexchange.com/?qa=3447/time-required-pass-electricity-through-electroplating-bath
<p>The time required to pass 3600 Coulomb of electricity through an electroplating bath using a current of 200 mA is <strong><strong>__</strong></strong>_ hours</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3447/time-required-pass-electricity-through-electroplating-bathWed, 17 Apr 2019 03:09:40 +0000Container filled with fluid move with a acceleration a
http://physics.qandaexchange.com/?qa=3446/container-filled-with-fluid-move-with-a-acceleration-a
<p><img src="https://i.imgur.com/2lDHr3Z.jpg" alt=""></p>
<p>My try : </p>
<p><img src="https://i.imgur.com/5rhhb1t.jpg" alt=""></p>
<p>My option B is not getting matched.<br>
Answer is given as B, C.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3446/container-filled-with-fluid-move-with-a-acceleration-aTue, 16 Apr 2019 15:23:24 +0000Calculating equivalent capacitance.
http://physics.qandaexchange.com/?qa=3442/calculating-equivalent-capacitance
<blockquote><p>A parallel plate capacitor of capacitance $C$ without dielectrics is filled by a dielectric slab as shown <a rel="nofollow" href="https://pasteboard.co/I9lgDqO.png">here</a>, the new capacitance will be?</p>
</blockquote>
<p><img src="https://i.imgur.com/lhSXbwo.png" alt=""></p>
<p>When I solve it in two ways as shown <a rel="nofollow" href="https://pasteboard.co/I9lhJYk.png">here</a> I got different results as $3.9C$ and $4C$ respectively, why? And which one is correct, please help.<br>
<img src="https://i.imgur.com/4gEkS5x.png" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3442/calculating-equivalent-capacitanceTue, 09 Apr 2019 13:46:03 +0000Velocity of image of submerged object when liquid surface moves
http://physics.qandaexchange.com/?qa=3437/velocity-image-submerged-object-when-liquid-surface-moves
<blockquote><p>Speed of the image (as seen by an observer in air) of the coin if the liquid surface is raised with speed $8\ m/s$<br>
<img src="https://i.imgur.com/jLiy7jG.png" alt=""><br>
I know how to deal with when the object is moving but how to do when surface moves?</p>
</blockquote>
Physics Problemshttp://physics.qandaexchange.com/?qa=3437/velocity-image-submerged-object-when-liquid-surface-movesMon, 08 Apr 2019 10:48:47 +0000Minimum force required to rotate a lamina when there is friction
http://physics.qandaexchange.com/?qa=3433/minimum-force-required-to-rotate-lamina-when-there-friction
<blockquote><p>A uniform right-angled lamina is placed on a horizontal floor which is not frictionless. One of the acute angles of the lamina is $\theta$. If $F_a$ and $F_b$ are the minimum forces required to rotate the lamina about stationary vertical axes through the vertices A and B respectively, find the minimum force required to rotate the lamina about a stationary vertical axis through the vertex C.</p>
</blockquote>
Physics Problemshttp://physics.qandaexchange.com/?qa=3433/minimum-force-required-to-rotate-lamina-when-there-frictionSat, 06 Apr 2019 06:54:35 +0000Increasing resistance with temperature.
http://physics.qandaexchange.com/?qa=3432/increasing-resistance-with-temperature
<blockquote><p>When a bulb, connected across potential $V$ of initial resistance $R_o$ is switched on its resistance increases due to heat production. Assuming initial temperatures of the bulb is $0^{\circ}C$, and temperature coefficient of the bulb is $\alpha$. After what time its temperature will become $T$. The heat capacity of the bulb is $c$.</p>
</blockquote>
<p>I only know that $R=R_o\cdot e^{\alpha\cdot (T_2-T_1)}$ how do I apply it here, please help?</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3432/increasing-resistance-with-temperatureWed, 03 Apr 2019 14:42:27 +0000Given the vector current density, determine the total current flowing outward through a circular band
http://physics.qandaexchange.com/?qa=3431/current-density-determine-current-flowing-outward-circular
<p>Given the vector current density, determine the total current flowing outward through a circular band.:</p>
<p><a rel="nofollow" href="https://i.stack.imgur.com/klQAo.png"><img src="https://i.stack.imgur.com/klQAo.png" alt="enter image description here"></a></p>
<p>The answer should be 518A. It comes something around 3255 A. Where is the mistake?</p>
<p><a rel="nofollow" href="https://i.stack.imgur.com/g1T1l.jpg"><img src="https://i.stack.imgur.com/g1T1l.jpg" alt="enter image description here"></a></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3431/current-density-determine-current-flowing-outward-circularFri, 29 Mar 2019 11:20:51 +0000Nucleon-Nucleon Scattering
http://physics.qandaexchange.com/?qa=3430/nucleon-nucleon-scattering
<p><img src="https://i.imgur.com/hZhT97F.png[/img]" alt=""><br>
<img src="https://i.imgur.com/rklrj0w.jpg[/img]" alt=""></p>
<p>I computed the orbital angular momentum classically, and then used quantum mechanics. But I am not convinced of what I got, because $L \alpha \sqrt{E}$ is a proportional equation that does not justify that when E < 20 MeV you get L ~ 0 (I do not see, numerically speaking, the difference between either plugging 20 MeV or 19MeV).</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3430/nucleon-nucleon-scatteringWed, 27 Mar 2019 12:38:33 +0000Where do I make the approximations in this proton and electron collision problem?
http://physics.qandaexchange.com/?qa=3407/where-make-approximations-proton-electron-collision-problem
<blockquote><p>A proton moving with a velocity $\beta c$ collides with a stationary electron of mass $m$ and knocks it off at an angle $\theta$ with the incident direction. Show that the energy imparted to the electron is approximately $$T \approx \frac{2\beta^2 \cos^2\theta}{1-\beta^2\cos^2\theta}mc^2$$</p>
</blockquote>
<p><em>Link to question :</em><br>
<a rel="nofollow" href="https://www.chegg.com/homework-help/questions-and-answers/proton-moving-velocity-collides-stationary-electron-mass-m-knocks-angle-incident-direction-q35643739?trackid=VRP2b2Jt">https://www.chegg.com/homework-help/questions-and-answers/proton-moving-velocity-collides-stationary-electron-mass-m-knocks-angle-incident-direction-q35643739?trackid=VRP2b2Jt</a></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3407/where-make-approximations-proton-electron-collision-problemSun, 17 Mar 2019 04:34:00 +0000How to apply the gauss law when charge density is a function of not only $r$?
http://physics.qandaexchange.com/?qa=3416/how-apply-the-gauss-law-when-charge-density-function-not-only
<p>The problem goes as </p>
<blockquote><p>A sphere of radius R, centre at origin carries charges with density $\rho(r,\theta)= \frac{KR(R-2r)sin\theta}{r^2}$ where K is a constant and $r,\theta$ are usual spherical co-ordinates. Find the potential and field for points on the $z$ axis far from the centre. </p>
</blockquote>
<p>Now in that question how can I apply Gauss' Law because the equipotential surfaces would not be sphere anymore? </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3416/how-apply-the-gauss-law-when-charge-density-function-not-onlySun, 17 Mar 2019 04:33:56 +0000Problem 5.13 Griffiths; Balancing magnetic attraction with electrical repulsion
http://physics.qandaexchange.com/?qa=3412/griffiths-balancing-magnetic-attraction-electrical-repulsion
<p><img src="https://i.imgur.com/FXLVcBI.png[/img]" alt=""></p>
<p><img src="https://i.imgur.com/PMivCmW.png[/img]" alt=""></p>
<p><img src="https://i.imgur.com/YY66H4H.png[/img]" alt=""></p>
<p>I do not get why it is argued that the balancing is impossible; in fact, we are working with line charges, which do travel at the speed of light. </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3412/griffiths-balancing-magnetic-attraction-electrical-repulsionThu, 14 Mar 2019 17:49:57 +0000Maximum charge and maximum current
http://physics.qandaexchange.com/?qa=3406/maximum-charge-and-maximum-current
<p><img src="https://i.imgur.com/KvunUGd.jpg" alt=""><br>
<img src="https://i.imgur.com/Am0TnRX.jpg" alt=""></p>
<p>My try :</p>
<p><img src="https://i.imgur.com/y81hQwo.jpg" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3406/maximum-charge-and-maximum-currentMon, 11 Mar 2019 01:57:30 +0000Griffiths 5.4 Force on a square loop
http://physics.qandaexchange.com/?qa=3404/griffiths-5-4-force-on-a-square-loop
<p><img src="https://i.imgur.com/HckbPJf.png[/img]" alt=""></p>
<p><img src="https://i.imgur.com/9SEg3Li.png[/img]" alt=""></p>
<p>Before doing any calculation, I see the net force being zero;</p>
<p>$$ F_{AB} = -F_{CD}$$</p>
<p>$$ F_{BC} = -F_{DA}$$ </p>
<p>But apparently this is not the case. The provided solution is:</p>
<p><img src="https://i.imgur.com/75ijztI.png[/img]" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3404/griffiths-5-4-force-on-a-square-loopSat, 09 Mar 2019 11:53:06 +0000How to induce large current in flexible wire and explaining how does it stretch into a circle
http://physics.qandaexchange.com/?qa=3401/induce-large-current-flexible-explaining-does-stretch-circle
<blockquote><p>The idea is to explain how could we induce current in a flexible loop using an initially free-of-current wire.</p>
</blockquote>
<p><strong>Some background.</strong></p>
<p>The current has to be the same all the way around (otherwise charge would be gathered at some point and in that accumulation of charge, the electric field would point in a way that the flow would even out). </p>
<p>The two forces involved in driving the current around the loop are the source force (typically a battery) and the electrostatic force, which smooths out the flow. The line integral of the vector sum of the previous forces is known as electromotive force (emf).</p>
<p><strong>My answer to the problem</strong> </p>
<p>My difficulty in this problem is that I do not have clear the sketch. I would say that the following happens:</p>
<p>Imagine that the loop is in the xy plane. The velocity of the current is tangential to the loop and its direction is clockwise; $B$ will point in the $-z$ direction and the force will point radially outwards. This force would be the source one (provided by the battery and the one that does work to move the loop; I know magnetic force does no work; the individual radial vectors of the force do work but the net work done by all of them is zero) if the wire were just connected to a battery. I also understand that the net electrostatic force is zero (this is a closed path).</p>
<p>But here there is no battery, the current is induced by a change in the current of the wire</p>
<p>My intuition tells me that is the change in the current of the wire what changes the flux of the wire and the changing flux induces the emf in the loop. But not really sure of this...</p>
<p><strong>What's the nature of the induced current in the loop?</strong></p>
<p><strong>EDIT:</strong> The original exercise does not provide details on the set up, but my interpretation was the following: we start with two free-of-current wires: one is a loop, the other a straight line. We apply current on the straight wire, which induces an emf on the loop (which will stretch into a circle; this idea came from one of the sources I checked: <a rel="nofollow" href="https://physics.stackexchange.com/questions/239591/magnetic-potential-energy">https://physics.stackexchange.com/questions/239591/magnetic-potential-energy</a> ).</p>
<p>Souces:</p>
<p><a rel="nofollow" href="https://physics.stackexchange.com/questions/239591/magnetic-potential-energy">https://physics.stackexchange.com/questions/239591/magnetic-potential-energy</a></p>
<p><a rel="nofollow" href="https://physics.stackexchange.com/questions/266895/what-force-causes-the-induced-emf-of-a-loop-and-the-difference-between-a-loop?rq=1">https://physics.stackexchange.com/questions/266895/what-force-causes-the-induced-emf-of-a-loop-and-the-difference-between-a-loop?rq=1</a></p>
<p>Introduction to Electrodynamics by David Griffiths</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3401/induce-large-current-flexible-explaining-does-stretch-circleFri, 08 Mar 2019 16:08:33 +0000question about 4-velocity
http://physics.qandaexchange.com/?qa=3396/question-about-4-velocity
<p>A particle is moving in the x, y plane at a speed of v = 0.80 and it is travelling an angle of 60 degrees<br>
above the x-axis.</p>
<p>(a) Rotate the spatial coordinates so that v lies along the x-axis and then construct the components of the 4-velocity for the particle.</p>
<p>(b) Construct the remaining orthonormal basis vectors for the particle in the rotated frame, then rotate the spatial coordinates back to find the basis vectors in the original frame.</p>
<p>(c) Perform the same steps above but this time begin by rotating the spatial coordinates so that <br>
v lies along the y-axis. Do you get the same result for the basis vectors after rotating back to the original frame? Should you? Draw a picture with ~v, the original (x, y) frame, and the two rotated frames to explain what is happening.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3396/question-about-4-velocityWed, 27 Feb 2019 22:32:29 +0000Electric field far away from a bunch of charges
http://physics.qandaexchange.com/?qa=3393/electric-field-far-away-from-a-bunch-of-charges
<p>I am given a bunch of charges and asked for the electric field at a field point far away (see image below).</p>
<p>What I would do is the following:</p>
<p><img src="https://i.imgur.com/UYHbwWv.jpg[/img]" alt=""></p>
<p>What I have done is applying Gauss' Law. However, in the lecture, another approach was used. </p>
<p>Firstly, the charges were treated per pairs , as dipoles. And as there are 4 +ive and 4 -ive, they cancel each other out and there is no first order contribution (i.e. $\frac{1}{r}$) .</p>
<p>Secondly, it was argued that this a quadrupole (using the same logic that above). Thus, the final answer would qualitatively be:</p>
<p>$$E \propto \frac{1}{r^3}$$ </p>
<p>Thus using two different methods one gets different answers; using method 1 one gets $E \propto \frac{1}{r^2}$ and using method 2 one gets $E \propto \frac{1}{r^3}$</p>
<p> Who is wrong and why? </p>
<p>Thanks.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3393/electric-field-far-away-from-a-bunch-of-chargesSun, 24 Feb 2019 20:14:51 +0000Find position and velocity at t=0?
http://physics.qandaexchange.com/?qa=3377/find-position-and-velocity-at-t-0
<p>Full question: </p>
<blockquote><p>An object moves with constant acceleration. At t= 2.50 s, the position of the object is x=2.00 m and its velocity is v= 4.50 m/s. At t= 7.00 s, v= -12.0 m/s. <br>
Find: <br>
(a) the position and the velocity at t= 0;<br>
(b) the average speed from 2.50s to 7.00 s, and <br>
(c) the average velocity from 2.50s to 7.00 s.</p>
</blockquote>
<p>I tried using the kinematic equations of motion for constant acceleration but my answers make no sense. </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3377/find-position-and-velocity-at-t-0Tue, 05 Feb 2019 00:03:55 +0000What is the fraction of work per second by F is converted into heat.
http://physics.qandaexchange.com/?qa=3373/what-is-the-fraction-of-work-per-second-by-converted-into-heat
<blockquote><p>Two long parallel horizontal rails, a distance l apart and each <br>
has a resistance $\lambda$ per unit length are joined at one end by a <br>
resistance R. A perfectly conducting rod MN of mass m is free to<br>
slide along the rails without friction. There is a uniform magnetic <br>
field of induction B normal to the plane of paper and directed <br>
into the paper. A variable force F is applied to the rod MN such <br>
that, as the rod moves, a constant current i flows through R. <br>
What is the fraction of work per second by F is converted into heat.<br>
<img src="https://i.imgur.com/u4AZz4a.png" alt=""></p>
</blockquote>
<p><img src="https://i.imgur.com/Ps83YAo.jpg" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3373/what-is-the-fraction-of-work-per-second-by-converted-into-heatWed, 30 Jan 2019 13:44:47 +0000Find minimum distance between dipoles
http://physics.qandaexchange.com/?qa=3372/find-minimum-distance-between-dipoles
<p><img src="https://i.imgur.com/qrx8ozT.jpg" alt=""></p>
<p>My try :</p>
<p><img src="https://i.imgur.com/SUmBmaA.jpg" alt=""><br>
<img src="https://i.imgur.com/Y4IFqfs.jpg" alt=""><br>
But answer does not match.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3372/find-minimum-distance-between-dipolesWed, 30 Jan 2019 13:32:57 +0000Force that one half of uniformly charged solid sphere exerts on other half - Griffith 2.43
http://physics.qandaexchange.com/?qa=3368/force-uniformly-charged-solid-sphere-exerts-other-griffith
<p><img src="https://cdn.pbrd.co/images/HYuG13c.png" alt=""></p>
<p>I got the result mentioned, by considering the electric field as $\dfrac{\rho\cdot \vec{r}}{3\epsilon_o}$, and integrating carefully.</p>
<p>As problem asks to calculate the force on one part due to other, but the electric field I'm using here is the result of complete solid non conducting sphere, so why are we considering $E$ of the northern hemisphere to calculate force <strong>it</strong> experience. </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3368/force-uniformly-charged-solid-sphere-exerts-other-griffithMon, 28 Jan 2019 06:18:15 +0000Electric field intensity at the centre of a solid hemisphere with uniform volume charge density
http://physics.qandaexchange.com/?qa=3360/electric-intensity-centre-hemisphere-uniform-volume-density
<p><img src="https://i.imgur.com/HtUlmlP.png" alt=""></p>
<p><a rel="nofollow" href="https://imgur.com/a/n0iohng">https://imgur.com/a/n0iohng</a></p>
<p>I am using Guru's Electromagneic Theory Fundamentals: <a rel="nofollow" href="https://www.amazon.ca/Electromagnetic-Field-Theory-Fundamentals-Singh/dp/0521116023">https://www.amazon.ca/Electromagnetic-Field-Theory-Fundamentals-Singh/dp/0521116023</a></p>
<p>For finding the electric field intensity, I am using the equation:<br>
<img src="https://i.imgur.com/G2nW912.png" alt=""><br>
<a rel="nofollow" href="https://imgur.com/a/RHS6SfY">https://imgur.com/a/RHS6SfY</a></p>
<p>I am unsure about what the value of r prime should be for a solid. </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3360/electric-intensity-centre-hemisphere-uniform-volume-densitySun, 20 Jan 2019 03:09:55 +0000Rotating ball inside rotating cylinder.
http://physics.qandaexchange.com/?qa=3359/rotating-ball-inside-rotating-cylinder
<p>How do I proof: <img src="https://cdn.pbrd.co/images/HWY3y5g.png" alt=""> </p>
<p>Textbook solution :<br>
<img src="https://cdn.pbrd.co/images/HXsICHVJ.png" alt=""><br>
<img src="https://i.imgur.com/jTOB86r.png" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3359/rotating-ball-inside-rotating-cylinderFri, 18 Jan 2019 05:18:03 +0000Frequency modes of the rectangular shell
http://physics.qandaexchange.com/?qa=3357/frequency-modes-of-the-rectangular-shell
<p>This is task i received from my professor:</p>
<blockquote><p>The shapes of three natural modes having the frequencies $\omega_1, \omega_2, \omega_3$ of the rectangular shell are presented in the figure. The exciting pressure $p(t)$ applied uniformly all over the one side of the shell has the form $p(t) = Pe^{jωt}$. <br>
Make a sketch of the normal displacement of the gravity point of the shell against frequency, if the excitation frequency varies within bounds $0.5\omega_1< \omega <2\omega_1$ and static displacement of that point equals to $u_0$.</p>
</blockquote>
<p>Links to photo of frequency nodes (sorry for low quality)-><a rel="nofollow" href="https://ibb.co/b1nh3j9">1</a> .</p>
<p>Can somebody help me and tell me how i should get started?</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3357/frequency-modes-of-the-rectangular-shellMon, 14 Jan 2019 21:42:44 +0000tension in wires from which a block is suspended
http://physics.qandaexchange.com/?qa=3349/tension-in-wires-from-which-a-block-is-suspended
<p><img src="https://cdn.pbrd.co/images/HVdTW5k.png" alt="1"></p>
<p>I am trying to figure out why the answer is T>W. Do you have any idea why? If so could you please explain. Thank you.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3349/tension-in-wires-from-which-a-block-is-suspendedSun, 06 Jan 2019 15:45:40 +0000How to solve this throwing ball off cliff question
http://physics.qandaexchange.com/?qa=3350/how-to-solve-this-throwing-ball-off-cliff-question
<p><img src="https://cdn.pbrd.co/images/HVdO2s0.png" alt=""></p>
<p>For b) I was curious why i couldn't use $s = ut + \frac12at^2$ as my equation as i had all the necessary known values. Instead to get the correct answer i had to use $v=u + at$.</p>
<p>Why is this so? Thank you for your time.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3350/how-to-solve-this-throwing-ball-off-cliff-questionSun, 06 Jan 2019 15:45:23 +0000Time period of small oscillation- disk and particle system
http://physics.qandaexchange.com/?qa=3346/time-period-of-small-oscillation-disk-and-particle-system
<p><img src="https://cdn.pbrd.co/images/HUWMQA2.jpg" alt=""></p>
<p>Attempt: </p>
<p>$y_{COM} = \dfrac{R}{3} = \dfrac {25}3$</p>
<p>$I = \dfrac 12 (2)R^2 + 1R^2 = 2\times 25 = 50 $</p>
<p>Now, T is given by: $T =2\pi \sqrt{\dfrac{I}{mgl}}$ where l is the distance of the centre of mass from the centre of rotation</p>
<p>So $T =2\pi \sqrt{\dfrac{50}{3 \times 10 \times \dfrac{25}{3}}} = 2\pi\sqrt{\dfrac{1}{5}}$</p>
<p>No option :( </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3346/time-period-of-small-oscillation-disk-and-particle-systemFri, 04 Jan 2019 22:33:35 +0000Wave optics- number of minimas.
http://physics.qandaexchange.com/?qa=3345/wave-optics-number-of-minimas
<p><img src="https://cdn.pbrd.co/images/HUWujTQ.jpg" alt=""></p>
<p>Attempt: </p>
<p>Let m be the integer associated with $420 nm$<br>
and n be the integer associated with $540 nm$</p>
<p>$d \sin \theta = k \lambda $ $k\in Z$<br>
Clearly, </p>
<p>$m_{max} = 180$ </p>
<p>$n_{max} = 140 $</p>
<p>$(2m+1) \lambda_1 = (2n+1)\lambda_2$ (condition for dark fringes to overlap)</p>
<p>$\implies \dfrac{2m+1}{2n+1} = \dfrac 97$</p>
<p>$\implies m = \dfrac{1+7n +2n }{7}$</p>
<p>Hence, we obtain, for m to be an integer: $2n+1 = 7k$</p>
<p>$\implies n = \dfrac{7k-1}{2}$ where $k \in Z$</p>
<p>Now note that k must be odd since odd-1 = even </p>
<p>Thus, using $n \le 140$, $k_{max} = 39$</p>
<p>Now, we have to consider only odd values of k which are $1,3,...39$ = 20 numbers </p>
<p>Thus, we have 20 minimas on the upper side and 20 on the lower,<br>
Total minimas = $20+20 = 40$</p>
<p>But answer is $D$</p>
<p><strong>Question 1:</strong> What is wrong with my method? </p>
<p><strong>Question 2:</strong> Considering that this is a JEE Mains problem, what is the fastest 2 minute way to do it? </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3345/wave-optics-number-of-minimasFri, 04 Jan 2019 22:01:11 +0000oblique collision of a rigid rod with a plane surface
http://physics.qandaexchange.com/?qa=3336/oblique-collision-of-a-rigid-rod-with-a-plane-surface
<blockquote><p>A uniform rod AB of length L is released from rest with AB inclined at angle 60° with horizontal, with the closer end of the rod to the ground, at a height 49m from it. Assuming the collision of the rod with the ground to be perfectly elastic, calculate the height the centre of mass of the rod will rebound after impact (assume ground to be frictionless).</p>
</blockquote>
Physics Problemshttp://physics.qandaexchange.com/?qa=3336/oblique-collision-of-a-rigid-rod-with-a-plane-surfaceTue, 01 Jan 2019 16:23:00 +0000Cylinder lying on conveyor belt
http://physics.qandaexchange.com/?qa=3323/cylinder-lying-on-conveyor-belt
<blockquote><p>You buy a bottle of water in the store and place it on the conveyor belt with the longitudinal axis perpendicular to the direction of movement of the belt. Initially, both the belt and the bottle are at rest. We can approach the bottle as one cylinder with radius $a$, mass $M$ and moment of inertia $I = M k^2$ ($k$ in units of length), in which the mass is not distributed uniformly. The speed of the belt at time $t$ is $V (t)$.<br>
a) Find an expression for the speed $v(t)$ of the centre of mass of the bottle.<br>
b) Explain why a bottle tends to start spinning on one moving band.</p>
</blockquote>
<p>What I have tried:</p>
<p>a) Having both longitudinal axis and belt's velocity vector perpendicular to each other <strong>on the same plane</strong> means that there will be rolling motion if we assume that static friction will be overcome. Let's disregard slippery effects as well.</p>
<p>Here I used an approach based on the fact that <strong>the bottle-belt-Earth system is nonisolated in terms of energy because the belt exerts an external force on the bottle, which means that it does work on the bottle.</strong> Therefore:</p>
<p>$$W = \Delta K_{tr} + \Delta K_{rot}$$</p>
<p>$$(F-f_f)d =v_{CM}^2 (\frac{I_{CM}}{a^2} + M)$$</p>
<p>$$v_{CM} = \sqrt{ \frac{2(F-f_f)d}{\frac{I_{CM}}{a^2} + M}} = \sqrt{ \frac{(F-f_f)d}{ M}}$$</p>
<p>The result I got does not seem to be incorrect; I checked dimensions and got $\frac{L}{T}$ .<strong>My question here is if I am right including the force F. I consider this force as a fictitious one, which is triggered by the non inertial frame in which the bottle is located: the conveyor belt.</strong> Note I am analysing the scenario from an inertial reference frame: The Earth (we regard it as inertial for known reasons). </p>
<p>b) If the static friction force was equal to the fictitious force F the cylinder <strong>would not spin</strong>. It would just move transitionally along the belt. Actually, if we were located on the belt, we would not see the cylinder move at all.</p>
<p><strong>In order to spin, the magnitude of F must exceed the magnitude of the maximum force of static friction. This friction force is recalled as force of kinetic friction.</strong></p>
<p><strong>EDIT</strong></p>
<p>From second (translation) Newton's law:</p>
<p>$$a_o= \frac{f}{M}$$</p>
<p>From second (rotation) Newton's law:</p>
<p>$$\tau = I \alpha = fa$$</p>
<p>$$k^2 \alpha= a_o a$$</p>
<p> $$\alpha = \frac{a_o a}{k^2}$$</p>
<p>Where $a_o$ is the acceleration of the cylinder measured from the ground.</p>
<p><strong>Assuming that the acceleration of the belt is constant</strong> ($a_b$):</p>
<p>$$ \frac{V}{t} = a_b$$</p>
<p>The acceleration of the cylinder with respect to the ground accounts for the acceleration of the belt and the angular acceleration of the cylinder (which has a negative sign because I considered the cylinder spinning clockwise i.e. the belt accelerating to the left and regarding that direction as the positive one). Therefore:</p>
<p>$$a_o = a_b - a\alpha$$</p>
<p>$$a_o = \frac{V}{t} -a\frac{a_o a}{k^2}$$</p>
<p>$$a_o = \frac{Vk^2}{(k^2 + a^2)t}$$</p>
<p>We know by kinematics that:</p>
<p>$$v_{cm} = \frac{Vk^2}{k^2 + a^2}$$</p>
<p>This makes sense to me. However I am confused because <strong>I was suggested that I should not assume that the belt moves with constant acceleration</strong> (please see kuruman's #2 comment <a rel="nofollow" href="https://www.physicsforums.com/threads/cylinder-lying-on-conveyor-belt.963471/">https://www.physicsforums.com/threads/cylinder-lying-on-conveyor-belt.963471/</a> ); Then how could I solve this problem?</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3323/cylinder-lying-on-conveyor-beltSat, 22 Dec 2018 16:56:04 +0000floating cubical block
http://physics.qandaexchange.com/?qa=3319/floating-cubical-block
<blockquote><p>A cubical block of copper of side $10\ cm$ is floating containing mercury. Water is poured into the vessel so that the coper in the block just gets submerged. The height of the water column is?</p>
</blockquote>
<p>Solution goes like :</p>
<blockquote><p>Let height of water column be $h$, then $$\rho_w gh + \rho_{Hg} g(10-h)=\rho_{Cu} g 10$$</p>
</blockquote>
<p>I don't understand this, why are they writing pressure using Mercury?</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3319/floating-cubical-blockThu, 20 Dec 2018 11:03:40 +0000Prove that the vector of acceleration always points towards the origin
http://physics.qandaexchange.com/?qa=3312/prove-that-vector-acceleration-always-points-towards-origin
<blockquote><p>A planet travels in an ellipse around the origin with the sun close to the origin. The planet's position in the ellipse is given by:</p>
<p>$x(t)=a\cos(kt)$</p>
<p>$y(t)=b\sin(kt)$</p>
<p>where $a>b$ and $k$ are constants and $0 ≤ t ≤ 2\pi$ ($t$ is a time variable).</p>
<p>The sun's position is given by $(x,y) = ( \sqrt{ a^2 − b^2}, 0)$.</p>
</blockquote>
<p>I've learnt that taking the derivative of the functions for position twice gives the functions for the acceleration. How would this look and how can I compare this answer with the functions for positions to show that the vector of acceleration is always pointed towards the origin?</p>
<p>In my attempt I've got that the acceleration is</p>
<p>$$a_x(t) = −ak^2cos(kt), a_y(t) = −bk^2sin(kt)$$</p>
<p>So the difference between position and acceleration is $−k^2$, provided that I'm correct so far. However I do not understand how this would show that the acceleration always is pointed towards the origin. Does the place of the sun even have any relevance? Considering that no masses and gravitation is taken account for.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3312/prove-that-vector-acceleration-always-points-towards-originSat, 15 Dec 2018 13:02:51 +0000Final charge on the capacitor and Charge on capacitor as a function time
http://physics.qandaexchange.com/?qa=3311/final-charge-the-capacitor-charge-capacitor-function-time
<p>In the given circuit diagram, initially charge on lower plate of capacitoris $Q_0$ = $CE/2$. Now switch is closed at t=0. Find<br>
1) Final charge on the capacitor<br>
2) Charge on capacitor asa a function time<br>
<img src="https://cdn.pbrd.co/images/HRxhcEy.jpg" alt=""></p>
<p>My try :<br>
<img src="https://cdn.pbrd.co/images/HRxhI0X.jpg" alt=""></p>
<p>In part b I tried to apply KVL but that would be quite lengthy.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3311/final-charge-the-capacitor-charge-capacitor-function-timeThu, 13 Dec 2018 12:16:20 +0000Check whether the followings are null, spacelike or timelike
http://physics.qandaexchange.com/?qa=3275/check-whether-the-followings-are-null-spacelike-or-timelike
<p>(a) <br>
$x^0=\int r^2+z^2d\tau$<br>
$x^1=\int r\sin\theta d\tau$<br>
$x^2=\int r\cos\theta d\tau$ <br>
$x^3=\int z d \tau$<br>
(b)<br>
$x^0= \sqrt3 ct$<br>
$x^1=ct$<br>
$x^2=ct_0 \sin(t/t_0)$<br>
$x^3=ct_0 \cos(t/t_0)$<br>
where $t_0$ is constant.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3275/check-whether-the-followings-are-null-spacelike-or-timelikeSun, 09 Dec 2018 11:01:29 +0000A projectile is ejected with vertical speed $v$ from the surface of a planet of mass $M$ and radius $R$
http://physics.qandaexchange.com/?qa=3295/projectile-ejected-with-vertical-speed-surface-planet-radius
<blockquote><p>A projectile is ejected with vertical speed $v$ from the surface of a planet of mass $M$ and radius $R$. Show that it comes to rest at a distance r from the centre of the planet where $$r=R/(1-Rv^2/2GM)$$ If $ v = c$ in the above example what will be the condition between M and R such that the planet acts like a Newtonian black hole.</p>
</blockquote>
<p>I have tried to solve it in the following way-</p>
<p>The height from the surface of the planet will be given by-<br>
$$y=vt-(1/2)gt^2$$<br>
when it comes to rest $v=0$ hence from the above equation we get<br>
$$r-R=(1/2)gt^2$$ <br>
From relation between g and G,<br>
$$g=Gm/r^2$$<br>
I have put all this values in $$y=vt-(1/2)gt^2$$<br>
but I am not getting the required answer. </p>
<p>Please tell me where did I made the mistake and correct me if going in the wrong direction. Thanking you. </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3295/projectile-ejected-with-vertical-speed-surface-planet-radiusSun, 09 Dec 2018 11:01:24 +0000Rotation of L shaped rods after impulse
http://physics.qandaexchange.com/?qa=3304/rotation-of-l-shaped-rods-after-impulse
<blockquote><p>Two identical rod each of mass $m$ and length $\ell$ joined at one end and<br>
free to rotate about this end kept on smooth horizontal surface. An<br>
horizontal impulse $J$ is given to rod AB at centre and perpendicular to<br>
rod AB.<br>
<img src="https://cdn.pbrd.co/images/HQEyifd.png" alt=""><br>
<img src="https://cdn.pbrd.co/images/HQEyzJS.png" alt=""></p>
</blockquote>
<p><img src="https://cdn.pbrd.co/images/HQEyNxw.jpg" alt=""><br>
I am just able to deal the angular velocity about centre of but unable to proceed for individual rods.</p>
<p>Unable to proceed for second part.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3304/rotation-of-l-shaped-rods-after-impulseFri, 07 Dec 2018 17:01:43 +0000System of two ideal Fermi gases in three dimensions.
http://physics.qandaexchange.com/?qa=3294/system-of-two-ideal-fermi-gases-in-three-dimensions
<blockquote><p>1) What is the pressure of a gas of free bosons in the limit of vanishing temperature, $T \rightarrow 0$?<br>
2)Argue that for $T \rightarrow 0$ an ideal Fermi gas will have non-vanishing pressure $p_0 > 0$. <br>
We will now use this fact to study a system of two ideal Fermi gases in three dimensions.<br>
A free sliding piston separates two compartments labeled 1 and 2 with volumes $V_1$ and $V_2$ respectively. An ideal Fermi gas with $N_1$ particles with spin 1/2 is placed in compartment 1 and an ideal Fermi gas with $N_2$ particles with spin 3/2 is placed in compartment 2.</p>
</blockquote>
<p><img src="https://cdn.pbrd.co/images/HPrUESc.png" alt=""></p>
<p><img src="https://cdn.pbrd.co/images/HPrVk3f.png" alt=""></p>
<p><img src="https://cdn.pbrd.co/images/HPrVAq7.png" alt=""></p>
<p>As you notice, this problem has already been solved, but I do not understand the vast majority of it.</p>
<p>1) is OK.</p>
<p>2) I do not know how they got equation 15. It is stated to be a continuous approximation but not idea how to even start. </p>
<p>Actually, Griffiths has an interesting section in which treats the fermion distribution:</p>
<p><img src="https://cdn.pbrd.co/images/HPs57DJ.jpg" alt=""></p>
<p><img src="https://cdn.pbrd.co/images/HPs7CTH.jpg" alt=""></p>
<p>I know that the Fermi Dirac distribution (which is the one which interests us, since we are working with fermions) has a pretty well-known behavior as $T \rightarrow 0$ (please see figure 5.8 in Griffiths).</p>
<p>But I still do not know how to get it. </p>
<p>From here on I simply got lost. I mean, I have studied the free particle in QM but they go on with the density of states from EQ 16... I do not grasp it.</p>
<p>May you please shed some light on the provided solution (from EQ 15)?</p>
<p><strong>EDIT:</strong></p>
<p>Now I am stuck at EQ 19.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3294/system-of-two-ideal-fermi-gases-in-three-dimensionsThu, 29 Nov 2018 19:49:17 +0000The lean of a motorcyclist
http://physics.qandaexchange.com/?qa=3273/the-lean-of-a-motorcyclist
<blockquote><p>A motorcyclist takes a turn with a radius of $500 m$. Both the mass of the engine and the motorcyclist is $160 kg$ and their centre of mass lies $0, 5 m$ above the ground when it is perfectly vertical. His tangential speed is $60 m / s$ and its tangential acceleration is $4 m / s^2$.</p>
</blockquote>
<blockquote><p>a) Make a clear drawing in top view and back view with the<br>
speeds, accelerations and forces that affect the engine and motorcyclist.<br>
b) Calculate the speed and acceleration of the motorcyclist.<br>
c) Calculate the size of the components of all forces that act on<br>
the contact surface of the engine with the road.<br>
d) Calculate the angle at which the motorcyclist takes the turn (Hint: take its<br>
mass centre as the origin of the system).<br>
e) What is the apparent weight of the motorcyclist when he turns?* </p>
</blockquote>
<p>What I have done and what I do not know:</p>
<p>a)</p>
<p>I was not sure about what <strong>'top view and back view'</strong> meant so I did the following:</p>
<p>This is the diagram analysed from above: <a rel="nofollow" href="https://imgur.com/a/JtpNmfr">https://imgur.com/a/JtpNmfr</a></p>
<p>This is the diagram analysed from the ground: <a rel="nofollow" href="https://imgur.com/a/9AwOrWa">https://imgur.com/a/9AwOrWa</a></p>
<p>Note that the forces have just been drawn on the latest diagram because of clarity purposes. </p>
<p><strong>Is there anything missing on the diagrams?</strong></p>
<p>b) </p>
<p><a rel="nofollow" href="https://imgur.com/a/bbcrmPm">https://imgur.com/a/bbcrmPm</a></p>
<p><a rel="nofollow" href="https://imgur.com/a/0wPegtU">https://imgur.com/a/0wPegtU</a></p>
<p>NOTE: I assumed uniform circular motion. <strong>It makes sense for you what I did?</strong></p>
<p><strong>EDIT</strong></p>
<p>I was wrong assuming uniform circular motion because there is tangential acceleration; <strong>the motorcycle does not move with uniform speed.</strong></p>
<p>c) </p>
<p>Here we just have to use Newton's second law:</p>
<p>$$\sum F = Ma$$</p>
<p>As we are under uniform circular motion:</p>
<p>$$F = M a_c = M \frac{u^2}{OB}$$</p>
<p>However, we are not asked for calculating the centripetal force but the ones exerted on the road and the engine (always including the person's mass). These are:</p>
<p>The force exerted on the road by the engine:</p>
<p>$$F = Mg = -1569,6 N$$</p>
<p>The force exerted on the engine by the road:</p>
<p>This is simply the reaction force (Newton's third law):</p>
<p>N = 1569,6 N</p>
<p><strong>This seems too simple, am I missing something?</strong></p>
<p>d)</p>
<p>I do not know how to calculate the angle properly. Actually I got:</p>
<p>$$\alpha = \frac{ut}{OB}$$</p>
<p>But depends on time. <strong>Should I use kinematics to get the time and therefore the angle?</strong></p>
<p>e)</p>
<p><strong>Isn't the apparent weight just the normal force exerted on the motorcyclist? (i.e N = 1569,6 N)?</strong></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3273/the-lean-of-a-motorcyclistSat, 24 Nov 2018 17:45:39 +0000Questions from a jumping kangaroo
http://physics.qandaexchange.com/?qa=3263/questions-from-a-jumping-kangaroo
<p><img src="http://i68.tinypic.com/2lc8wnn.jpg" alt=""></p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3263/questions-from-a-jumping-kangarooFri, 16 Nov 2018 15:38:20 +0000SHM with elastic collision.
http://physics.qandaexchange.com/?qa=3260/shm-with-elastic-collision
<blockquote><p>A ball suspended by a thread of length $l$ at the point $O$ on the wall, forming a small angle $\alpha$ with the vertical <a rel="nofollow" href="https://imgur.com/Ytg3szH">(Fig.)</a>. Then the thread with the ball deviated through a small angle $\beta$ $(\beta>\alpha)$ and set free. Assuming the collision of the ball with the wall to be perfectly elastic, find the oscillation period of such a pendulum.</p>
</blockquote>
<p><img src="https://i.imgur.com/g9zeh4t.png[/img]" alt=""></p>
<p>From <a rel="nofollow" href="https://imgur.com/a/7PTbF5W">fig</a> $2\theta$ part of SHM will be skipped over, $\cos\theta=\dfrac{\alpha}{\beta}\implies\cos2\theta=\dfrac{2\alpha^2-\beta^2}{\beta^2}$. So time it would be skpping over will be $t=\dfrac{1}{\omega}\cos^{-1}\bigg(\dfrac{2\alpha^2-\beta^2}{\beta^2}\bigg)$. On substrating from total time $T=2\pi\sqrt{\dfrac{l}{g}}$ gives me $T'=2\sqrt{\dfrac{l}{g}}\bigg[\dfrac{\pi}{2}+\sin^{-1}\bigg(\dfrac{2\alpha^2-\beta^2}{\beta^2}\bigg)\bigg]$. But in official answer argument of sin inverse is $\dfrac{\alpha}{\beta}$.</p>
<p>Please help.</p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3260/shm-with-elastic-collisionFri, 16 Nov 2018 13:31:41 +0000Diffusion with reflecting boundary
http://physics.qandaexchange.com/?qa=3254/diffusion-with-reflecting-boundary
<p><img src="https://cdn.pbrd.co/images/HNaMhdt.png" alt=""></p>
<p>What I have tried:</p>
<p><img src="https://cdn.pbrd.co/images/HNaMSPP.jpg" alt=""></p>
<p><img src="https://i.imgur.com/hls9bU5.png" alt=""></p>
<p>Note that my question is that how is it possible that I get $t = \infty$. It does not make sense for me (physically speaking). Where did I get wrong?</p>
<p>Please if there is information you require let me know. </p>
Physics Problemshttp://physics.qandaexchange.com/?qa=3254/diffusion-with-reflecting-boundaryWed, 14 Nov 2018 20:07:35 +0000