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  1. D

    Quantum Harmonic Oscillator

    You are missing an x^2 in #3.
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    Variable mass system - sand falling on flatcar

    F=ma can be applied, but that will only make the problem more complex. If you apply it to (flatcar + sand on it), you need to find the forces acting on the system. Sand falling on the flatcar exerts a force to it, because friction has to act on the sand to accelerate it until its velocity equals...
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    Efficiency of a engine

    Thanks for the reply. Now the problem is solved. Diesel cycle - Wikipedia, the free encyclopedia
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    Efficiency of a engine

    Homework Statement Four thermodynamic processes A,B,C,D are shown in the picture. A and C are adiabatic processes. Pressure is held constant during B, and volume is constant during D. An engine run from A->B->C->D->... What is the efficiency of this engine (in terms of V1/V2)? Homework...
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    Integrating dx/dt=k(a-x)(b-x)

    In the original post. t=0 when x=0.
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    Magnetic Induction (Non-uniform Current)

    Because J is a function of radius. I=\int { J\cdot dA } The second method looks fine. For the second question: What is the enclosed current outside? Is it zero?
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    Integrating dx/dt=k(a-x)(b-x)

    Looks like I get x=\frac { a{ e }^{ r }-b }{ { e }^{ r }-1 } \\ r=(b-a)(kt+c)
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    Integrating dx/dt=k(a-x)(b-x)

    What are the values of a,b, and k?
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    Question about Eötvös experiment

    Thanks a lot for the link. I will read them.
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    Question about Eötvös experiment

    I do not understand the concept. Let the centrifugal forces on the two objects are F1 and F2. The rod will not rotate because net torque is 0. That is, F1r1=F2r2. That Does that mean we have to carefully adjust the positions of objects (before experiment) so that m1gr1=m2gr2? Then we conclude...
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    Help with piston and atmospheric pressure

    P1 is the initial pressure. Look at the piston. There is a upward force produced by air inside, which equals P1 times S. Two downward forces are atmospheric pressure and weight. This gives the first equation, and the second one is similar.
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    Finding max. velocity of jet w/ constant and/or changing acceleration

    In the case when mass changes (because of fuel), F=ma no longer helps. Try F=dP/dt
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    Triangle Inequality Proof

    Write down the triangle inequality. You need a minus sign, which can be obtained by moving something to the other side of the inequality.
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    Finding the maximum acceleration of a crank.

    Consider a small angle (delta theta) at the top of circle, and another one at the bottom. The rod length and angular velocity are constant. So moving through those two sections (two small angles at top and bottom) takes same time. But how much distance does the crank move? Looks different. So...
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    Finding the maximum acceleration of a crank.

    Sorry, I seemed to forgot that minus sign and messed up something. Your calculation is correct. cos\theta +(cos2\theta /n) has a range from -353/480 to 19/15, which is shown in the link. Put that back into the equation gives...
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    Finding the maximum acceleration of a crank.

    It looks like the acceleration varies with crank angle. Putting θ = 1 (rad) into the formula gives the acceleration at that particular position, not the maximum value. I get 113.96 m/s^2 as the maximum acceleration from your formula. I think that's close but not very accurate, because that...
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    Tank filled with liquid, help?

    Use Bernoulli's equation and continuity equation.
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    Messy double integral

    Why not u=x, v=2y?
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    Angles of a triangle

    You may need this formula: 3sinx-4{ sin }^{ 3 }x=sin3x Edit: It is possible to solve it directly using Cardano's method: