Part 3 (10 points) : ddot(x) = g m / (M + m + alpha m_p)

   100 %: practically perfect
    90 %: correct except a sign error
    90 %: correct except for a (small) numerical error
    80 %: forgot to include the kinetic energy for m (or M)
    80 %: dimensional error in the answer
    80 %: gravity applied to one extra mass (such as M), leading to an
          incorrect answer
    60 %: gravity applied to all masses, leading to an incorrect answer
    40 %: the answer is not fully developed

Part 3-extra (5 points) : friction = - mg alpha m_p / (M + m + alpha m_p)

   100 %: practically perfect
    95 %: would have been perfect, were it not for (numerical) mistakes
          accumulated from previous part(s)
    90 %: correct except for a (small) numerical error
     0 %: answer missing, or completely incorrect

Part 4 (10 points) : ddot(x) = (1 + gamma) m g / ((1+gamma) (M+m) + gamma
                     m_b),  ddot(s) = gamma ddot(x) / (1 + gamma)

   100 %: practically perfect
    99 %: used the correct constraint, but its discussion shows lack of
          clarity
    80 %: correct constraint was used, but error in step
    60 %: the correct constraint and an unnecessary incorrect constraint
          were used together
    50 %: incorrect constraint was used
    40 %: the answer is not fully developed
    33 %: gravity applied to all masses and incorrect constraint used
    33 %: incorrect constraint used, and the kinetic energy for m (or M)
          not included
     0 %: answer missing, or completely incorrect

Part 4-extra (5 points) : friction = - mg gamma m_b / ((1+gamma)(M+m) +
                          gamma m_b)

   100 %: practically perfect
    95 %: would have been perfect, were it not for (numerical) mistakes
          accumulated from previous part(s)
    50 %: incorrect constraint was used
    40 %: the answer is not fully developed
    33 %: incorrect constraint used, and the kinetic energy for m not
          included
    10 %: some discussion is presented, but no clear direction is indicated
     0 %: answer missing, or completely incorrect