Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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1answer
32 views

Capillary rise for a tube with a glass rod [closed]

Take a capillary tube (glass) of diameter $d_2$ dipped in water vertically. Now a glass rod with diameter $d_1$ is inserted in the tube. Find the height to which the water rises. Take contact angle to ...
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0answers
88 views

Net Force on a System [closed]

In the figure given below is a system of a mass M ,a pulley and 2 masses of mass m. Now there is friction between bodies A and C and B and C. A force ($ F$) is applied in such a way that body C is a ...
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1answer
48 views

What is the radiation pressure on sphere of radius $r$? [closed]

Consider a planet with luminosity $L$ and a sphere of radius $r$ which is localized at a distance $d$ away from the planet. I would like to compute the radiation pressure that the planet exerts on ...
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1answer
68 views

Classical Mechanics: spring + mass + cylinder [closed]

I am trying to solve this problem and I am using this lagrangian but I can not solve it: $$ \mathcal{L} = \frac{1}{2}(m+M)\dot{x}^2 - m\dot{x}\dot{\theta}R\cos(\theta) +\frac{1}{2}mR^2\dot{\theta}^2\...
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0answers
37 views

Parametric Geodesics of a 2-sphere

The geodesic equations of a 2-sphere are the following: $$\ddot\theta - \sin\theta \cos\theta\dot\phi = 0$$ $$\ddot\phi + 2\cot(\theta)\dot\theta \dot\phi = 0$$ For $\theta$=$\pi$/2, $\phi(s)$=a$s$+b. ...
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1answer
25 views

Work and Energy question, using Tension

Given this image, $2$ objects are connected via a spring (its mass is negligible) The spring constant is $k$ and that is all that is given.. mass of $A$ is just $m_A$ etc.. and $g \approx 9.8 \frac{m}{...
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0answers
27 views

Physics pendulum problems [closed]

Mr A has a bucket of water suspended from a fixed point by a rope.Mr A set the bucket in such a motion that the system swings like a pendulum. But the bucket leaks and the water slowly flows out of ...
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1answer
33 views

Physics puzzle problems [closed]

Mr A always reaches station at 3 pm and Mr B picks him with his bicycle and takes him home. One day Mr A reached 1 hour earlier than usual time at the station and started walking towards home. He took ...
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0answers
33 views

Momentum of An Object [closed]

If four horizontal forces F1=3N F2=6N F3=3N AND F4=6N is applied on a body of mass 5 kg. If force F3 is removed ,then find the value of rate of change of momentum
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0answers
46 views

Question concerning a problem of Morin‘s book: Introduction to classical mechanics [closed]

The question from the book is the following: A rope wraps an angle $\theta$ around a pole. You grab one end and pull with a tension $T_0$. The other end is attached to a large object, say, a boat. If ...
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0answers
19 views

A fighter jet making a vertical circular motion [closed]

A fighter jet making a vertical circular motion with radius of 3 km at speed of 230 m's. If the mass of the pilot is 60 kg, find the normal force on the pilot at the top and lowest point.
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1answer
22 views

Friction on a wire (angle of repose) [closed]

A wire is molded into a shape in vertical plane as shown. The equation is given by $y=0.5\sin 2x$. A bead B can slide on the wire.The coefficient of friction between bead B and wire is $0.5$. The ...
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0answers
37 views

Problem with symmetry and integral of motion in Classical Mechanics [closed]

I am currently working through the problem 4.10 in Kotkin and Serbo's book "Collection of Problems in Classical Mechanics". The problem consists in showing that the quantity \begin{equation} ...
1
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2answers
64 views

What happens in Newtonian mechanics when a particle reaches infinite force position?

Suppose a particle of negligible mass is placed at e.g. $x=1$ inside a one dimensional space with a force field generated by the gravitational attraction of a point mass at the origin $0$. I.e. the ...
1
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1answer
38 views

How to identify internal and external forces acting on a system of particles?

In my Physics textbook there is sample problem in which a firecracker placed inside a coconut of mass M, initially at rest on a frictionless floor, blows the coconut into three pieces (A, B and C) ...
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0answers
25 views

Measuring through Vernier Caliper

A vernier caliper has $10$ divisions on the main scale and $9$ divisions on the vernier scale. The main scale and the vernier scale are both made of a material whose coefficient of linear expansion is ...
0
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1answer
31 views

Torque and inverted pendulum

I'm supposed to derive a relationship in which the change in gravity $\delta g$ is linked to the change in length of the spring $\delta s$. When the beam is tilted due to increased weight or gravity, ...
3
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2answers
94 views

How is the first Friedmann equation derived from Einstein's field equations?

I see that Friedmann's first Equation (for flat space) is: $$\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi G}{3}\rho.$$ And I know that Einstein's equation, just considering the time-time component is: $...
0
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1answer
39 views

Expansion in spring with two masses at its end [closed]

Two solid spheres (mass and radius may be considered same or different by the one who answers) are connected by a spring with spring constant $k$ and the entire setup is on a surface with coefficient ...
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0answers
20 views

The Effect of Extremely Heavy Rain being driven by Hurricane force winds [closed]

Situation: A very large ship, 300m length, loaded with containers. The ship is berthed alongside a quay. Windage area of the ships side is 8000 sqm. The ship is held alongside by a total of 7 ropes ...
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0answers
33 views

Push up question in physics [closed]

how can I calculate F3 when the mass is 69 kg
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0answers
44 views

Projectile motion:How are we gonna do this? [closed]

particle from ground passes two points which are heights h1=12m h2=18m above the ground and a distance d=10m apart. what would be the minimum speed of projection.(g=10m/s2) I got that we can resolve ...
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1answer
74 views

Approximating the energy levels of the anharmonic oscillator using WKB

I got stuck trying to solve this problem: Given the potential $$V(x) = \frac{m\omega^2x^2}{2}-\beta x^4,\ \beta>0$$ I need to evaluate the deviation of the energy levels from the harmonic ...
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0answers
35 views

Consider a liquid drop of radius $R=\frac{1}{π} mm$ [closed]

Consider a liquid drop of radius $R=\frac{1}{π} mm$ . The surface tension of the liquid is $T=9×{10}^{2}$ and it is electrically insulating. Keeping the radius fixed, the surface of the drop is ...
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1answer
33 views

I am confused about resolving of forces in a certain situation. Where am I wrong?

I was solving questions related to circular motion of a pendulum hanging from a ceiling in an inertial frame having angular displacement $θ$ and if I resolve Tension into vertical and horizontal ...
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0answers
14 views

How do I explain the photoelectric effect using ideas of photons, conservation of energy and work function? [closed]

Basing the question on the fact that electromagnetic waves interaact with matter as photons, how do I answer this? Thank you.
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1answer
39 views

Dielectric and capacitor

During my course on dielectrics in capacitors, I learned that the dielectric medium if inserted between the plates of a capacitor, reduces the electric field from $E_0$ to $\frac{E_0}{K}$, $K$ being ...
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4answers
2k views

Is geothermal energy ultimately derived from solar energy?

The following question is taken from 10th class science NCERT book chapter 14th. Most of the sources of energy we use represent stored solar energy. Which of the following is not ultimately derived ...
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0answers
15 views

Exhaustible versus Non-Renewable Resources [closed]

The following question is taken from 10th class science NCERT book chapter 14th. Differentiate between exhaustible, inexhaustible, renewable and non-renewable resources. Exhaustible- which can ...
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0answers
24 views

Displacement of A point in a rolling wheel problem [closed]

In the picture attached above, Radius of the wheel, $r=45\;\text{cm}$ A point "A" is located in the wheel is on the plane intially. The wheel rolls $210^\circ$ forward and comes to a final ...
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0answers
27 views

Finding the rate of a river current by using the quadratic formula [closed]

A man can row ${ 20 }$ miles downstream and back in ${ 7.5 }$ hours. If his rate of rowing in still water is ${ 6mph }$, find the rate of the stream. Supposedly there is a way to solve this using ...
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1answer
23 views

How do I calculate the acceleration using kinematic equations? [closed]

A bike accelerates uniformly from rest to a speed of $7.10\ m/s$ over a distance of $35.4\ m$. Determine the acceleration of the bike. (Hint: Use a kinematic equation) I am given the speed and the ...
0
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1answer
104 views

Analytical Solution to Heat Equations

I have the steady state equation with an internal source as $$\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2k\frac{\partial T}{\partial r}\right)+Q=0$$ which has the analytic solution $$T(r)=-\frac{...
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2answers
62 views

Inner and outer ring, Biot-Savart law [closed]

So basically I have an inner ring with radius $R_2$ and an outer ring with radius $R_1$, with current $I_0$ flowing through the outer ring. I am asked to evaluate the magnetic field strength at the ...
0
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1answer
57 views

Gravitation: Collision of a satellite and Meteorite [closed]

A satellite is orbiting around a planet in a circular path of radius $R$. A meteorite of mass $m$ collides with the satellite and sticks to the satellite. After collision, the satellite is seen to ...
3
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0answers
93 views

Weyl Anomaly Derivation in Polchinski Eq (3.4.21)

In Polchinski's longer derivation of the Weyl anomaly, he arrives at the result (equation 3.4.19): $$ \ln{\frac{Z[g]}{Z[\delta]}} = \frac{a_1}{8\pi} \int d^2\sigma \int d^2\sigma' g^{1/2} R(\sigma) G(\...
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1answer
43 views

Speed of particles in an exploded asteroid

An asteroid of mass $M$ explodes into a spherical homogeneous cloud in free space. Due to energy received by the explosion the cloud expands and the expansion is spherically symmetric. At an instant ...
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2answers
32 views

Pressure at the bottom of a container

Before I ask my question, I would like to clarify that this is NOT a homework question. Rather I would like to clear up an issue with my intuition about fluid statics using this problem. Firstly, I ...
0
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2answers
89 views

Behaviour of capacitor right after switch is closed [closed]

The flip S is closed, find charge flown from P to Q So I know at end behaviour of circuit, it should be just $ 15 uC$ just by applying kirchoff voltage law. Initially before switch is flipped, the ...
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1answer
29 views

Springs: How does a stiffer spring slow mass acting upon it versus a lighter spring? [closed]

If I have a mass of $11.6$ ounces moving at $6.88$ fps, how does a stiffer spring react to this force versus a lighter spring of the same length—e.g. will a stiffer spring make the impact softer? Will ...
0
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1answer
37 views

Physical quantities conversion

searching for experimental values of the consumption rate of $O_2$ by tumor cells I found an article that measures the rate in the units of measure $$\frac{mol}{cell\cdot s}.$$ The actual measurement ...
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0answers
29 views

Does anyone know how the equation was derived from the given conditions?

When the operators are multiplied together, the term f(hw)g(hw)aa or f*(hw)g*(hw)aa will be kept. But why those terms disappear in the Green function given below?
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0answers
30 views

How will Decreasing Velocity Affect Time Dilation? [duplicate]

Imagine that we have two observers, named $O_1$ and $O_2$. $O_1$ is traveling at a velocity of $\frac{c}{2}$ for $60$ seconds while $O_2$ is completely still. According to the equation for time ...
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0answers
25 views

How do I calculate the maximum separation between a chord and arc when I only know the length of each? [migrated]

If I know the length of a chord and I know the length of an arc that both have the same starting and ending points (A and B), how do I calculate the maximum separation between them? (D and D1) What is ...
0
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1answer
63 views

Proof that $U$ is an unitary operator [closed]

I have a function $f$ mapping a bit onto another bit, i.e. $f : \{0, 1\} \rightarrow \{0, 1\} $. The function f is either constant, so f(0) = f(1) or balanced, so f(0) $\neq$ $f$(1). The quantum gate ...
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2answers
41 views

Independence of kinetic energy with respect to $\rho$ when potential energy is independent of $\phi$

Reference material (free access right now): Shankar On page 81 of Shankar, (paraphrasing) he states that: $ 1: T$, the kinetic energy in polar coordinates, depends solely on $\frac{d}{dt} \phi$ if $\...
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2answers
63 views

Time Dilation + Length Contraction Scenario

I was bored today and went on a random learning binge (I haven't touched this topic before today in a good decade since high school), and got stuck with this scenario I created for myself: [I let ...
2
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2answers
620 views

Is this a Taylor approximation? How is it done? [closed]

I know what a Taylor series involves but you have to know the function; here $\mathcal{L}^*$ is just a function depending on $(v+w)^2$, any kind of function could be inside. How can the below ...
0
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1answer
35 views

Functional variation problem in Classical Field Theory (Non Relativistic) [closed]

An exercise of my Homework sheet make a statement about rotational variation on a scalar field $\phi(x)$:\ "Consider a scalar field $\phi(x,t)$ in a lagrangian $\mathcal{L}(\phi, \partial_t \phi, ...