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    Entery level Mass-energy equivalence questions

    The increase in kinetic energy must have come from a reduction in rest mass. In other words the mass of the two alphas is less than the mass of X and the proton. You have values for the rest mass of the alphas and the proton and the mass equivalent of the kinetic energy gained.
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    Entery level Mass-energy equivalence questions

    For question 1 find the difference between the initial kinetic energy and the final kinetic energy. Then use E=mc^2 to convert energy to a mass equivalent.
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    Starship special relativity problem

    There is nothing wrong with this calculation. All velocities relative to the observer are below c. It appears that the projectile has a relative velocity to the station of 1.1c from the ship's view but this is ok becuase relative to the ship all velocities are less than c. The velocity of the...
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    Starship special relativity problem

    I get -3.31s for the space station clock, not +3.31s. Is a negative or positive answer?
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    Entery level Mass-energy equivalence questions

    The guiding principle is mass/energy conservation. initial (rest mass energy + kinetic energy)= final (rest mass energy + kinetic energy) Question 1 is just concerned with the increase of kinetic energy expressed as a mass equivalence. Question 2 just use the above equation. Be careful to...
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    Lorentz transformations combined with force

    I would agree with what you have said. However you are perhaps expected to say something more about the cyclotron. Even at non-relativistic speeds r increases with v. However r is directly proportional to v and since time for 1 rev=2∏r/v the frequency of revolution is a constant which...
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    Help differentiating energy wrt time.

    I was thinking L was the extension of the springs when at equilibrium and x was the displacement from equilibrium. Anyhow it does not matter much since the constants drop out during differentiation.
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    Proton enters magnetic field in spiral trajectory

    The pitch of a spiral is the distance moved after one complete revolution. The diagram in section 2.5 of this wiki article is fairly clear:- The two velocity components would be vsinθ perpendicular to B vcosθ parallel to B vsinθ should be used...
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    Resonant frequencies in a tube with adjustable length

    I think unfortunately this question as stated is meaningless. Tuning forks only make one frequency so why is the question asking about the quantity of resonant frequencies? This has misdirected your thinking. If the question actually is asking " at what lengths of tube up to 1m does...
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    Shortest possible period of revolution of two identical gravitating solid spheres

    The 2 is correct. I got 16 because I used r=1/2 separation of masses. When cubed in the final equation this leads to a factor of 8 difference. 2 x 8 =16
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    Finding and labeling equilibrium points between multiple point charges.

    One approach might be to make an equation for the electric potential. Because potential is a scalar this is easier than trying to find an equation for force or field strength, which would require vector addition. Now field strength is equal to -potential gradient (E=-dV/dr or more generally...
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    Help differentiating energy wrt time.

    E = 1/2 mv^2 + k(x-l)^2 + 2k(l-x)^2 -mgx - don't think this is quite right I am guessing that we have one spring above the mass and one below? The terms for elastic spring energy are based on 1/2ke^2. Where e is spring extension. Isn't the extension of the springs l+x and l-x? Are...
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    Shortest possible period of revolution of two identical gravitating solid spheres

    You should be using r/2 in this equation to be consistent with your definition of r.
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    Mass on the wedge

    I sort of agree with you but would quibble over the wording. The resultant force is always given by ma. When going up the slope a=g(sinα+μ*cosα) But when going down a=g(sinα-μ*cosα) Resultant F=ma=mg*sinα+ reaction force from plates. Reaction force from plates=±mgμ*cosα So when going...
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    Special Relativity, calculating velocity of Kl0 meson with reference frames

    t' is indeed 5x10^-8. We know the kaons travel 45m in time t in the lab frame. So 45=vt and t=gamma t'. So 45=gamma x t' x v. Now solve for v.
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    Shortest possible period of revolution of two identical gravitating solid spheres

    let r= distance between centre of sphere and midpoint between spheres. then distance between centres of spheres=2r We then get F=-\frac{Gm^2}{4r^2}=-\frac{mv^2}{r} which simplifies to \frac{Gm}{4r}=v^2 Subbing in v^2=\frac{4\pi^2 r^2}{T^2} leads to T=(\frac{16\pi^2r^3}{Gm})^{1/2}
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    Help with projectile motion

    Yep that's the right answer. That is all that was needed.
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    Help with projectile motion

    19.94 is a component of the initial 22m/s. Draw a right angled triangle with 22 on the hypotenuse, 19.94 on the adjacent side and work out the angle.
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    Help with projectile motion

    Horizontally the ball moves 165.5m in 8.3s. What is the horizontal speed?
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    Calculate the kinetic energy of an electron with a wavelength of 1fm

    I agree with your method. In this case the energy is so much greater than rest energy that E≈pc is a good approximation of the answer.
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    Help with projectile motion

    You could start with speed= distance /time. Then think about components of velocity.
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    Thermal conduction between difference surfaces

    Sorry I should have stated that I was assuming that the situation had settled to a steady equilibrium situation. Indeed initially heat will flow faster through the more conductive material. This will change the temperature at the interface until the temperature gradient in the less conductive...
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    Shortest possible period of revolution of two identical gravitating solid spheres

    You should get T=(\frac{16\pi^2r^3}{Gm})^{1/2} With r being the distance between the centre of a sphere and the midpoint about which the spheres rotate. Now I suspect you need to replace the mass m with density x volume of a sphere. This introduces another distance: the radius of the...
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    Radiant Intensity vs. Irradiance

    Let a source of light give 1mW/sr. The Irradiance at 1cm away is 1mW/cm2 At 2 cm away it is 0.25mW/cm2 At 10cm away it is 0.01mW/cm2 This is because area subtended by solid angle = solid angle in steradians x distance squared.
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    Thermal conduction between difference surfaces

    Essentially I agree with what you have said. To add some more detail it might be useful to consider this equation \frac{ΔQ}{Δt}=-kA\frac{Δθ}{Δx} This basically says that the rate of flow of heat through a material depends on the conductivity times the contact area times the temperature...
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    Block on a slope, friction related

    In your attempt you've added the two vector components together as if they are scalar quantities ie 1006 + 2765 = 3771. I suggest you draw a free body force diagram for the 300kg block. Are we to assume it is on the point moving upwards?
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    Pedagogical machine

    I analyzed it from the stationary frame where all masses share a common acceleration and got the same results. I dislike working with pseudo forces because it encourages engineers to believe centrifugal forces are real.:grumpy:
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    Shortest possible period of revolution of two identical gravitating solid spheres

    Your final equation suggests that as r tends to infinity then T tends to zero. Does that sound reasonable? Your method is essentially right but you have got errors in the details of your equations. Applying Newton's law of gravity gives a force of F=-\frac{Gm^2}{r_d^2} Which should be...
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    Considering the -ve sign in Gravitational Potentail Energy

    Wiki says:-In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of gravity to move an object to a fixed reference location. By fixed reference location they mean infinity. It is the work done by...