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  1. B

    Linear algebra proofs

    where did the c come from, and why did you get rid of the t^2 in front of the w but not in front of the v,w
  2. B

    Linear algebra proofs

    i'm not sure how to go from P to PP, how do i explain what i'm doing i really don't understand the projection matrix thing for (a) , i don't know how to solve it still, i just know that I am using the proj formula, and doing it twice, but why is that the same as proj^2 like you said, i don't...
  3. B

    Linear algebra proofs

    okay so i understand the fact that we have the same thing, but how do i proceed from there? drawing it on paper, i know that it is 0, but i cannot prove this algebraically still, i am still stuck in the same place
  4. B

    Linear algebra proofs

    P = aa^T/(a^T a) = aa^T/||a||^2 i don't understand this at all, can you please explain this
  5. B

    Linear algebra proofs

    I'm going to use . as dot product To Prove: proj u (proj u (v)) = proj u (v) proj u ((u.v / u.u) u) = proj u ((u.v / |u|^2) u) = [u . (u.v/ |u|^2)u ]u / u.u = [u . (u.v/ |u|^2)u ]u / |u|^2 and i'm stuck here
  6. B

    Linear algebra proofs

    and i wasn't taught a specific way to do projections, just the formula itself.
  7. B

    Linear algebra proofs

    okay so for (b) i have expanded and collected the terms. q(t) = v\bulletv + v\bullettw + tw\bulletv + tw\bullettw q(t) = |v|^2 + 2(v\bullettw) + |tw|^2 so do i use the hint and say that in order for q(t) >= 0 it must satisfy a>0 and b^2-4ac <=0 which it does. but what about to show...
  8. B

    Linear algebra proofs

    i have to prove (a) algebraically, i can prove it with diagram and words, but not algebraically, i am having troubel doin that
  9. B

    Linear algebra proofs

    (a)Let u be a nonzero vector in R^{n}. For all v\epsilonR^{n}, show that proj_{u}(proj_{u}(v)) = proj_{u}(v) and proj_{u}(v - proj_{u}(v)) = \vec{0} (b) An alternate proof of the Cauchy-Schwarz inequality. For v,w \epsilonR^{n}, consider the function q: R -> R defined by q(t) =...
  10. B

    Mass center problem 2

    i dont understand why the bottom is pi a^2, it didnt say newhere in the question that the mass equals its area
  11. B

    Mass center problem

    i dont really understand whats wrong with it but here is the diagram, i guess i did miss this http://img63.imageshack.us/img63/9140/phys27rv.jpg [Broken]
  12. B

    Mass center problem 2

    question: find the location of the center of mass for the following disk of radius a. it has a three circular cut outs. one with a diameter of a and the other two have a diameter of b. http://img479.imageshack.us/img479/2743/physics4ld.jpg [Broken] solution: Xc = m/m(Xo - a/2) Xc = Xo -...
  13. B

    Mass center problem

    question: three uniform disks of the same mass per unit area, and radii a, 2a, 3a are placed in contact with each other with their centers on a straight line. how far is the center of mass of the system from the center of the smallest disk? solution: m1=pi a^2 m2=4pi a^2 m3=9pi a^2 Xc...
  14. B

    Friction problem with pulleys

    actually i have a question, i used 2Ft in one of the equations, and im wondering if this is right. for this step i used 2Ft : for the mass 2 fbd, i got Fg - 2Ft = ma2 (is it 2Ft???)
  15. B

    Friction problem (mass on top of another mass)

    for (a) i found the Ff of m1 by: Ff = ma Ff = 4(5.2) Ff = 20.8 mew (u) = Ff/Fn u = 20.8/(4)(9.8) u = 0.53 so for (b) the u k = 1/2 (0.53) = 0.265 am i right for (a)? and (b), i've no idea how to start
  16. B

    Friction problem with pulleys

    so, a2 = 0.30m/s / 0.80m = 0.375 m/s^2 and then sub it in to get Ff = 0.856 N oops, thats not the acceleraton hmm, u need kinematics?? is the veloctiy given v1 or v2 a = 9.8 m/s^2 d= 0.80 if velocity given is v2, so v1 = 0?
  17. B

    Friction problem on cube of mass

    okay, this is what i got so far, i dont know if its right. correct me if i had a mistake taking xaxis is // to side of funnel, and yais is perpendicular to side of funnel, i drew fbd and the forces i got are x components : Fs, - mg cos theta y components : Fn, - mg sin theta so i hvae...
  18. B

    Friction problem with pulleys

    ohh. okay, i did it like u said, but now im stuck for the mass 1 fbd, i got Ft - Ff = a1 for the mass 2 fbd, i got Fg - 2Ft = ma2 (is it 2Ft???) then isolate for a2 4.9 - 2Ft = 0.5a2 9.8 - 4Ft = a2 and the equaion from fbd #1: Ft - Ff = ma1 since a1 = 2a2 Ft - Ff = 4a2 (1) then i substituted...
  19. B

    Friction problem with pulleys

    The block with mass m2=0.50kg is found to have a speed of 0.30m/s after it has dropped 0.80m. how large a (kinetic) friction force retards the motion of the block with mass m1=2.0kg? (side note from teacher) To solve this problem, you can use a string constraint. the total length of the...
  20. B

    Friction problem (mass on top of another mass)

    a block with mass m1=4.0kg is placed on top of a block with mass m2=12.0kg. (a) if the acceleration of the lower block is a2=5.2m/s^2, calculate the minimum coefficient of static friction (u minimum, where u is mew), for the contact surface between 1 and 2, that will prevent block 1 from...
  21. B

    Friction problem on cube of mass

    a very small cube of mass m is placed on the inside wall of a funnel. The wall of the funnel makes an angle theta with the vertical axis of rotation (dotted line). The center of the cube is a distance r from the axis of rotation. the cube is held by static friciton. The funnel is then rotated...
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