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• 50.6k
Accepted

What law of thermodynamics is broken here?

This is not a good question. Yes, as stated, the engine appears to violate the first law. It can also be claimed that the second law is violated, but this is not that straightforward because some of ...
• 7,257
Accepted

Dependence (or lack thereof) of forces on frames of reference

When you say "blocks A and B move with a relative acceleration of -3 m/s2" you are considering the motion of one block in the reference frame attached to the other block (block C). But the ...
• 6,196
Accepted

A question regarding equations of motion

The equations of motion only work for constant acceleration. The setup mentioned in your question doesn’t satisfy that criteria. You can use the equations of motion to model the motion of the body ...
Accepted

Electric field inside a dielectric sphere placed in a uniform electric field

The solution presented in Griffiths follows a fully systematic method. At the very end, Griffiths makes the comment that "the field inside the sphere is (surprisingly) uniform". Now, the ...
• 4,585
Accepted

Why $\omega=vR$ can not be applied in this question?

It's $v = R\omega$, not $\omega = Rv$.
• 7,257

A question regarding equations of motion

v=0 after it hits the ground,SUVAT only applies when acceleration is uniform, when it hits the ground acceleration must change from 9.81 to something else, because there is now a new force acting on ...
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• 23k
1 vote

Gauss' Law in differential form applied to charged sphere

I think this problem is ill posed. The divergence operator is not generally invertible. There are many functions with the same divergence. We need further information of electric field on a region of ...
• 5,239
1 vote

An ideal gas expands into vacuum in an insulated rigid vessel. Which of the followings happens?

I think this could be their point of view, consider a rigid vessel with two chambers seperated by a partition. In this vessel, one of the chambers is filled with the ideal gas and the other chamber is ...
• 252
1 vote

How to calculate the moment of inertia of convex polygon? (two-dimensions)

Any polygon can be divided into triangles, as shown. With the common vertex at the origin. Then you need to find the centroid of the area (equal to C of G in this case). To do this, firstly calculate ...
• 577
1 vote

I will try to complement the answer by Thomas, since some things were not that clear to me. We start by varying the Lagrangian $\mathcal{L}(\phi(x),\partial_{\mu}\phi(x),x^{\mu}):$ $$\begin{split}\... • 1,164 1 vote Accepted Phase Difference of A Mass-Spring System For Different Starting Points I put the different phase values in a table to make this easier to talk about. The position can L,0,R meaning left, center and right and the velocity can be L,0,R meaning moving to the left, ... 1 vote How do I find the constraint relation in this question? The speed of the connecting belt must be twice the downward speed of the center of the lower pulley. This means that α_1 = 2 α_2. Then: mg – T – t = ma = mr α_2 where, T, is the connecting ... • 11.4k 1 vote Do prescribed glasses transmit light? Without light transmission, you will not be able to see anything since light is the way of transmitting the picture to your eye. 1 vote Different values for the Normal ordering Hint: In Wick's theorem what remains in the fully contracted term (= the double contration) is the unit-operator \hat{\bf 1} not the zero-operator \hat{\bf 0}, so OP's 1st calculation (v3) is ... • 167k 1 vote Regarding Griffith quantum mechanics problem 2.47: Square double well Consider the limits  b \to \infty  and  b\to 0  separately. In the limit  b \to \infty  the two wells are isolated from each other and the result is each particle does not interact with each ... • 3,606 1 vote Problem with possibly infinite possible solutions I don't see any obvious problems with your analysis. This problem appears to be statically indeterminate. If so, the "real" value of the tension would be determined by knowing the material ... 1 vote Accepted Kinetic energy of system consisting of rod and rolling cylinder When setting up the kinetic energy in terms of generalized coordinates, it is in many instances easiest to write$$ T = T_\text{tr,cm} + T_\text{rot,cm} $$where T_\text{tr,cm} is the translational ... 1 vote Accepted For virtual displacement in the Lagrangian, why is \delta \dot{x_i} = \delta \frac{dx_i}{dt} = \frac{d}{dt}\delta x_i \equiv 0? Generally speaking, you must consider a displacement with \delta x_i to be t-dependent, when applying the principle of least action. The section where \delta\dot{x}_i = 0 is about symmetries of ... • 391 1 vote Accepted Contravariant Vector Component Transformation from Polar to Cartesian It's because basis are defined with satisfying normalization condition. Basis are covariant, because they are partial derivatives(Consider them as gradient).$$\hat{r} = \frac{\partial}{\partial r} = ...
• 193

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