IB Physics. Coulomb’s law. Four Point Charges

Four equal point charges are placed on a straight line of length 2a. Two of the charges are fixed at the ends of the line. Find the positions on the line where the other two charges are placed if they are to be at rest. (From D. J. Griffiths and Y. Li, Am. J. Phys., 64, 6, June 1996, p 708) Answer is at x = ± 0.36148a from the centre of the line.

IB Physics. The Jumping Hoop

This tutorial sheet is about the jumping hoop demonstration. A smooth vertical hoop of mass M has two beads of mass m slotted on it, both initially at rest side by side at the highest point of the hoop. The masses are released and slide down along the hoop. Find the smallest ratio of m/M if the hoop is to leave the ground during the subsequent motion. (Problem given in Isaac Physics, L. Jardine-Wright, Periphyseos Press, 2015, p24)

  1. What is the first step in solving a mechanics problem? Draw a diagram showing the forces acting and the coordinates used.
  2. Is total energy conserved as the beads slide on the hoop?
  3. Is the linear momentum of the system conserved as the beads slide on the hoop?
  4. Is the angular momentum of the system conserved as the beads slide?
  5. What condition determines if the hoop leaves the surface?
  6. Answer. Ratio = 3/2.