Problem Set 4

Physics 5200

Due 23 Feb. 1999

  1. (2 points) Calculate the acceleration of a point on a wheel rolling at constant velocity (example 1.10.3 in the text, and discussed in lecture). Graph the position, velocity and acceleration for one revolution of the wheel.
  2. (3 points) A buzzing fly moves in a helical path given by the equation
    r(t) = ib sinw t + jb cosw t + kct2
    Show that the magnitude of the acceleration of the fly is constant, given that b, w , and c are constant.
  3. (2 points) Find the forces for each of the following potential energy functions:
    1. V = ax2 + by2 + cz2
    2. V = axyz + c
    3. V = a ln(x2 + y2 + z2)
    4. V = d exp(ax2 + by2 + cz2)
  4. (3 points) Find the value of the constant c such that each of the following forces is conservative:
    1. F = ixy + jcx2 + kz3
    2. F = i(z/y) + cj(xz/y2) + k(x/y)