IB Physics Static Friction

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A tutorial sheet on static friction, a concept in the HL and SL courses that is often misunderstood. These are “show that” questions requiring all steps with explanation and a labelled diagram to obtain full marks.

A rough cube of edge length a and weight W is placed on a rough horizontal surface. An identical second rough cube of weight W is placed on top of the first cube. The coefficient of static friction between each surface is µ. A horizontal force F is applied perpendicular to the cubes at a height h above the top of the bottom cube. Show that

  1. the lower cube does not slide along the horizontal plane if F < 2µW,
  2. the upper cube does not slide over the lower cube if F < µW,
  3. the lower cube does not topple if F < aW/(a+h),
  4. the upper cube does not topple if F < aW/(2h).

With h = a/2 the force F is now increased steadily from zero. Show that

  1. If µ < 2/3 equilibrium is broken by the upper cube sliding,
  2. If µ > 2/3 equilibrium is broken by the lower cube toppling.