IB Physics Topic A Tutorial Sheet : Block on an Incline

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A tutorial sheet on Topic A SL/HL that practices the concepts of motion, momentum, force and energy. There are “show that” questions that require a labelled diagram with all steps shown and “explain” questions that require elaboration involving the laws of Physics to obtain full marks in each case.

A block of mass m is placed on the hypotenuse of a smooth wedge of mass M and base angle 𝜃 that rests on a smooth horizontal surface.

The wedge is held at rest by a horizontal force F acting perpendicular to its vertical side.

  1. Show that the acceleration of the block of mass m as it slides down the wedge is gsin𝜃.
  2. Show that the normal force between the sliding mass and the wedge is mgcos𝜃.
  3. Show that the normal force between the horizontal surface and the wedge is g(M+m cos2𝜃)
  4. Show that F = mgcos𝜃 sin𝜃.
  5. Show that the time taken by the block to slide a distance L from rest is t = √( 2L/( g sin𝜃 ) ).

The block stays at rest relative to the wedge when a new force F acts perpendicular to the vertical side of the wedge.

  1. Show that the acceleration of the block is the same as the acceleration of the wedge.
  2. Show that the normal force between the block and the wedge is N = mg/cos𝜃.
  3. Show that the resultant force acting on the block is Nsin𝜃.
  4. Show that the acceleration of the block is gtan𝜃.
  5. Show that F = (M+m)gtan𝜃.

The block is released from rest on the smooth stationary wedge which has a hypotenuse of length L.

  1. Is linear momentum conserved as the block slides down the wedge? Explain why the wedge moves to the left if the block has a velocity component to the right.
  2. Explain why kinetic energy conserved is not conserved as the block slides down the wedge.
  3. Explain why energy conserved as the block slides down the wedge?
  4. The block is released from rest at a vertical height H. At a certain instant the height of the block is h and the horizontal and vertical velocity components of the block and wedge are (Vx,Vy) and (W,0) respectively. Write down the equations for conservation of linear momentum and energy.
  5. HL Show that the acceleration of the wedge is - mg sin𝜃 cos𝜃/(M + m sin2𝜃 ).
  6. HL Show that the time taken for the block to travel down the wedge is √2L ( (M + m sin2𝜃) /(g (M+m) sin𝜃) ). Show that the limiting case of m/M → 0 gives t = √( 2L/( g sin𝜃 ) ).