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77 views

How much energy is necessary to set a year to exactly 360 days

How much energy would be necessary to slow down Earth rotation such that a year was 360 days long? In the same spirit: how much energy would be necessary to make the Earth rotate faster around the ...
1
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2answers
41 views

Finding the current in a parallel circuit [closed]

Two resistors are joined as shown. The top resistor receives a current of 3 A. What is the current in the other resistor? What is the current that enters at junction A? I'm confused on how the two ...
0
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0answers
28 views

Calculus of variations applied to a rotating liquid

I thought I knew how to use calculus of variations, but then I started thinking about the problem of a rotating liquid and it confused me a great deal. It would be nice to hear your thoughts on the ...
3
votes
1answer
148 views

How is weight distributed when legs are astride?

Is there a simple and quick formula to find the weight (the force acting) on each leg, especially when legs are astride and they are not equally stretched? (or, better) not equally distant from the ...
2
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0answers
85 views

Hoop rolling inside a circular hole

A hoop of radius $b$ and mass $m$ rolls without slipping within a stationary circular hole of radius $a > b$ and is subject to gravity. Use the generalized coordinates the rotation angle $\phi$ of ...
3
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3answers
88 views

How to prove the Levi-Civita contraction?

I want to prove the following relation \begin{align} \epsilon_{ijk}\epsilon^{pqk} = \delta_{i}^{p}\delta_{j}^{q}-\delta_{i}^{q}\delta_{j}^{p} \end{align} I tried expanding the sum \begin{align} ...
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1answer
70 views

Finding the magnetic vector potential by calculus of variations

Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field ...
2
votes
1answer
109 views

Add air resistance to projectile motion

I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals. This is what I have so far: If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, ...
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1answer
36 views

Ways of finding average accelleration

So I had a little debate with a professor on a simple problem of motion (See section). It basically comes down to how to find average acceleration. I did some research and couldn't find a definite ...
2
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1answer
56 views

Motion with damping involving both $-v^2$ and $-v$ terms

I'm trying to solve for the motion of a particle, accounting for both viscous and drag forces. (There is no potential) The total resistance by medium is modeled by: $\vec{F}=-(\mu_1v + ...
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0answers
9 views

Prove scalar product is distributive [migrated]

The scalar product is defined as r*s = the sum of all r*s. Using this definition, prove that r*(u+v) = r*u + r*v. Also, if r and s are vectors that depend on time, prove that the product rule for ...
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1answer
28 views

Am I solving this basic Kirchoff's current law and Ohm's law problem correctly?

After moving onto some of the practice textbook exercises in the section covering Kirchhoff's current law and Ohm's law, I came across a problem which evades my best attempts at solving it. Using ...
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1answer
29 views

What's wrong with this solution to freshman textbook example for Ohm's law and Kirchhoff's current law?

I'm a freshman taking an introductory course on circuit theory and I've run into a bit of trouble working through a textbook example practice problem. Unfortunately, it only lists the answer and not ...
0
votes
1answer
31 views

Average acceleration when more than two different velocities occur [closed]

Suppose a car travels at 5m/s north for 5 seconds, it then turn east and travel at 7m/s for 10 seconds, finally it turns north east and travel at 10 m/s for 20 seconds. What is the average ...
2
votes
1answer
53 views

Current in an RC circuit inside in a magnetic field

Does my question make any sense? Context: The capacitor is charged with charge $Q_0$. There is a magnetic field $B=B_0 \hat{z}$ perpendicular to the monitor's screen. The length of the (AB) wire is ...
2
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0answers
73 views

How to calculate this functional derivative? [migrated]

How can I calculate the functional derivative of this functional? $$F[x(t)] = \int_{0}^{t}x(t_1)a(t_1)\left \{ \int_{0}^{t_1}x(t_2)b(t_2) \,dt_2\right \} dt_1 .$$ Where $a(t)$ and $b(t)$ are real ...
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3answers
166 views

Two runners on two different tracks

I got a question from a textbook, as follows. On two different tracks, the winners of the one-kilometer race ran their races in 147.95 seconds and 148.15 seconds. In order to conclude that the ...
0
votes
1answer
35 views

Coulombs law: calculate force exerted on one charge by the other two [closed]

The drawing shows three point charges fixed in place. The charge at the coordinate origin has a value of q1 = +8.00 μC; the other two charges have identical magnitudes, but opposite signs: q2 = ...
4
votes
2answers
80 views

Can we explicitly solve the Hamilton–Jacobi equation for a particle in a uniform magnetic field?

HJE for nonrelativistic charged particle in an electromagnetic field is $$\frac{1}{2m}\left(\nabla S - q\mathbf{A}\right)^2 + q\phi + \frac{\partial S}{\partial t} = 0.$$ For a uniform magnetic ...
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0answers
28 views

Coriolis deflection:- is it 4 times if the object is thrown up, compared to a drop?

A particle is thrown up vertically with initial speed, reaches a maximum height and falls back to ground. Show that the Coriolis deflection when it again reaches the ground is opposite in ...
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2answers
36 views

Problem finding the average velocity [closed]

Problem: A car travels along a straight line for first half time with speed of 40 km/h and second half time with speed 60 km/h. The mean speed of the car is__________. My answer: 48 km/h Why? ...
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2answers
39 views

Prove Biot-Savart law, assuming that $\vec{A}=\frac I c\int \frac{d\vec{L}}{r}$

Prove Biot-Savart law, assuming that $$\vec{A}=\frac I c\int \frac{d\vec{L}}{r}$$ $$\vec{B}=\nabla\times \vec{A}$$ Any hint on what to do next?
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0answers
54 views

Integrating with respect to time a double derivative $\ddot\phi + \frac bm\dot\phi = \frac{F}{mr}$ [migrated]

$$\ddot\phi + \frac bm\dot\phi = \frac{F}{mr}$$ I want to integrate this to get an equation for $\dot\phi(t)$ but I don't know how to integrate double derivatives. The answers say that the ...
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0answers
38 views

How to get the pressure? [closed]

A system of solar panels are fixed on top of a large water tank of height $40m$ and area $10m^2$. Atmospheric pressure is $100kPa$. What is the pressure at the bottom of the tank? The density of water ...
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1answer
25 views

Finding directions of the internal forces within a freely jointed rigid object?

Consider the the following problem: Here is a force diagram showing the situation: For part (i) Taking moments about $B$ for $BC$ gives $84.5Lcos\beta=2LT$ So $T=39$N For part (ii) Resolving ...
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1answer
33 views

Decelerating car [closed]

A car crashes into a immovable barrier at 60mph. (a)If the front-end of the car crumples a distance of 1.5 m in the collision, what is the deceleration experienced by the occupants? (Express your ...
0
votes
1answer
66 views

Relative velocity of two cars [closed]

Two cars A and B are at $100\,\text{m}$ and $200\,\text{m}$ distance from the origin $O$ at time $t = 0$. They start simultaneously with velocities $10\,\text{m/s}$ and $5\,\text{m/s}$ respectively. ...
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0answers
74 views

Geodesic deviation on a unit sphere

Very little interest in the original version of this question so I've rejigged it hoping for a more positive response. I'm trying to use the geodesic deviation ...
2
votes
0answers
26 views

Calculate signal strength received by an Ultrasonic Transducer [closed]

Below is an image showing transducer A transmitting a signal with an amplitude of 3000mV, I am trying to calculate the amplitude of the signal received by transducer B in mV, I understand that there ...
0
votes
1answer
42 views

Calculate minimum energy of incident neutrino using Mandelstam variables

I am studying the following nuclear reaction: $v + \tilde{v}\rightarrow Z^0$ where the antineutrino is motionless and has a given mass. The $Z^0$ boson has also a known mass. I'm trying to calculate ...
0
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1answer
64 views

How to compute speed without knowing mass or charge values?

A gold nucleus is 460 fm (1 fm = 10^(-15) m) from a proton, which initially is at rest. When the proton is released, it speeds away because of the repulsion that it experiences due to the charge on ...
0
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1answer
30 views

Alignment of a system in equilibrium and its potential energy

Consider a flexible free conductor which is placed near a strong long bar magnet. How will the the conductor arrange itself if current is passed through it? I asked my professor: he gave me a hint ...
0
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1answer
32 views

Electrostatics Equilibrium problem [closed]

What should be the value of Q? I am doing the basics of coulomb's law,can anyone explain this to me?
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2answers
62 views

How can I split a resultant force into its $x$ and $y$ components?

Point charge 3.5μC is located at x = 0, y = 0.30 m, point charge -3.5μC is located at x = 0 y = -0.30 m. What are (a)the magnitude and (b)direction of the total electric force that these charges ...
3
votes
1answer
754 views

How cold would a bowling ball near absolute zero make a room?

If a bowling ball at absolute zero suddenly appeared in my room, how cold would the room get? Would I die? My initial estimation is that it one bowling ball at 0K (i.e., 300K below room temperature) ...
1
vote
0answers
27 views

Sun reaching zenith at a particular latitude

I need to find when the sun reaches the Zenith at a given latitude. What I've done so far: $L=23.5 \cdot \sin(\frac{2\pi}{365.25}\cdot D) $ Here L is the latitude (<23.5) and D is number of days ...
0
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2answers
33 views

How do I write the units for this answer? [closed]

If the force (at 90∘ to the lever arm) applied is 15 N and it is applied at 2.0 m from the pivot point (point of rotation), what is the torque on the lever? Is it 30.0 N/m?
2
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1answer
42 views

Weight held by jet stream of water

Consider a bucket of weight $W$, held in air by a jet stream of water from the ground (moving vertically upwards) at height $h$. The water is fired from the ground at the rate of $\mu$ (units ...
1
vote
1answer
28 views

Gravitational Potential Energy to Kinetic Energy

When a yo-yo is released from a height $h$, the gravitational potential energy is converted to kinetic energy. However, the yo-yo obviously has less acceleration than $g$, $9.8\frac{m}{s}$. This means ...
2
votes
1answer
154 views

Is work is equal to $mv^2$ (without $\frac{1}{2}$)?

I was trying to come up with an equation for work that doesn't include time, because I don't know time. Here's what I did: $$ work = Fd = mad = m{v\over t}d = m{v\over\left({d\over v}\right)}d = ...
1
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0answers
67 views

Show that the profile of the hill is a cycloid [closed]

I'm struggling with this problem: From George Simmons_ Differential Equations I've tried different things and I showed that the $x$ component and the $y$ component of the shadow should move with ...
3
votes
0answers
32 views

Equivalent Dose absorption from Na22 source

No idea what exactly the rules are or how I should ask this question, but here's the verbatim quesiton: "A Na$^{22}$ source has an activity of 100 $ \mu $C. If you handle the source, how big is the ...
0
votes
1answer
103 views

What distance does one travels in his lifetime? [closed]

I think this isn't answerable without having point of reference from which speed at which earth travels in space, however if I am wrong the please give absolute distance. Considering that earth spins ...
0
votes
1answer
29 views

A Conversion problem featuring Significant figures [closed]

What is the speed of a car going v=1.000 mile per hour in SI units? You can do each conversion separately. Use the facts that 1mile=1609 meters and 1hour=3600 seconds. Express your answer in meters ...
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0answers
21 views

Unsure how resistors are connected? (Series/Parallel) [duplicate]

I am currently attempting this practice question in my tutorial and while I am able to reduce the circuit below to I do not know whether the 6/6/6/6 pane is connected in series or parallel, it ...
1
vote
1answer
54 views

Resistors in para and series circuit, finding volt [closed]

How anyone know how to do the question? I know how to reduce it to a window pane of 6/6/6/6 with a 3 in series but i have no idea how to do it. Well i did manage to reduce the right side of the ...
4
votes
3answers
110 views

Different results to a basic question ( Newton's law and perservation of momentum)

Trolley with mass of $m_0=1 \ kg$ is moving without friction on the railway track. It is raining so there is a constant mass flow of water $\Phi_m=0.1\ kg/s$. Constant force $F=0.1 \ N$ is ...
0
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1answer
59 views

A moving inclined plane with block problem

I'm trying to solve for a challenging problem : a moving inclined plane with a block I want to solve for the acceleration components for the block and the plane and the normal force acting on the ...
0
votes
2answers
49 views

equivalent spring constant for a drum floating in water

If I have a drum floating in water, how do I find the equivalent spring constant? I know that the water has density $\rho$, the drum has diameter $d$ and height $\ell$, and the positive direction is ...
0
votes
1answer
36 views

Deviation from 2D trajectory

I need to find out how far a ball is from the predicted trajectory in 2 dimensional space and I know the start and end position of the ball in both dimensions. Along with that I know the initial ...