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  1. Moara

    Static structure - find a fourth relation

    First, since A and B are articulated, the moments due to A and B are zero. Now, we may call reaction forces in A, ##V_A## and ##H_A## and in the same way, call the reactions in B as ##V_B## and ##H_B##. With that and Newton's third law, I managed to find three equations (equilibrium of...
  2. Moara

    Conditional probability and criminal DNA analysis

    We know that ##P(A-) = (95\% \cdot 0.5\% + 5\% \cdot 98.5\% )## and ##P(guilty \ and \ A-) = (95\% \cdot 0.5\%)##, so letter a) is just ##P(guilty \ and \ A-)/P(A-)##. What I tried to do in letter b) was again using the conditional probability theorem. First calculating the probability that...
  3. Moara

    Observation of events and analysis of the associated Hypotheses

    For letter a), i think that he is assuming that each hypothesis is independent, and that they are mutually exclusive. For letter b), I understand that it indeed admits the relative frequency interpretation, since the the experiment is being produced several times. For letter c) we do the...
  4. Moara

    LaTeX Program or platform for figures and diagrams

    When using latex for writing problems in physics, I find it difficult to make diagrams or figures (such as circuits, atwood machines, lenses, ...) so I wonder if anyone has some recommendations of programs or platforms that can make this "drawings" easy, possibly without the necessity of coding...
  5. Moara

    Wire rotating inside a magnetic field

    For a infinitesimal wire of lengh dx, the induced potential difference in an uniform B field perpendicular to it's motion is : dE=B.Vp.dx, where Vp is the component of the velocity perpendicular to the wire. Looking to the big wire I tried to take an arbitrary point express dE in function of...
  6. Moara

    Electron moving inside a region of homogeneous electric field

    a) since the eletric field is perpendicular to the inicial velocity, the x component is constant, hence Vf.cos45=Vo. This gives Vf=0,6√2.C b) Ei=γi.Eo , γi=5/4 , Ef=γf.Eo , γf=5/(2√7) Finally, Ei+e.E.d=Ef. Apparently this is incorrect, why??
  7. Moara

    Spherical gas distributed symmetricaly over space

    . We have that energy in a infinitesimal Spherical layer with number of mols dn is: dU=Cv.T.dn (1) But by the ideal gas law: PV=nRT (2) Differentiation gives: PdV+VdP=RTdn (3) (3) in (1) and using CV=3R/2 (monoatomic) gives: dU=3/2.(PdV+VdP) (4) Integration of (4) over the whole gas will...
  8. Moara

    Flux of Electric Field through a cone

    Since there is no charge inside the cone, the total flux through its surface is zero, hence Ø(lateral surface)+∅(base surface)=0. But ∅(base surface)=E.πR².cosΩ, because electric Field is homogenous. But by the figure, Ω is just arctg(h/R). So Ø(lateral surface)=-E.π.R².R/√(R²+h²). This is not...
  9. Moara

    Probability of hitting a rotating disc

    There are two points of the smaller disck such that a line is tangent to the two discks and passes by that point. If the particle leaves of any point belongin to the arch that connects these two points, then it will hit the other disck. So I managed to calculate the value of this arch and divide...
  10. Moara

    Eletromagnetism: Copper Plate on a Spring Oscillating in a Magnetic Field

    Tried to find the resultant force, but I can't see how the magnetic field affects. I used Faraday's law to find the the diferece of potentials in the plate Wich should be B.d.v, where v is the vertical velocity of plate, but there were not given the resistance or resistivity to relate with the...
  11. Moara

    Mass-spring system

    For the maximum elongation the velocities of the blocks should be equal. With that i used two conservation of energy for m1 and m2, for m1 the work of the elastic force is integral of kx(dx1) and for m2 kx(dx2), where X1+x2=x. I got three equation and four variables since i dont know the final...
  12. Moara

    Electric field of a charged cube

    Tried to use gauss law but there isn't any usefull symmetry that I have seen. Also tried to integrate the field due to small charges over the whole cube, didn't work too since the integral were too much complicated.
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