Notes on using Friction2.xls

This spreadsheet allows students to explore a mathematical model of block on a rough horizontal surface being acted upon by a variable force P acting at a variable angle. The mass of the block is fixed but the value of µ can be set between 0 and 2.

The aim is to develop further the understanding of the law of friction a brief reminder of which is included in the workbook. Students can then go on to investigate the minimum force P required to break equilibrium.

Background: Newton’s laws of motion and the law of friction. Resolving forces.

To fully explain the findings for the minimum P an understanding of the addition formula in trigonometry and how to optimise a function of the form acosq +bsinq.

Questions for students:

• Set µ equal to 0.5 and the angle of P equal to 0.

  • Use the spreadsheet to find the value of P required for limiting equilibrium.

  • Verify this value by calculation.

• Set µ equal to 0.5 and the angle of P equal to 50.

  • Click on the animate button near P to see the effect of increasing P while keeping the angle constant. What do you notice?

  • Explain the behavior of the reaction force R and the Frictional force Fr.

• Set µ equal to 0.5 and the angle of P equal to 50.

  • Use the spreadsheet to find the value of P required for limiting equilibrium.

  • By resolving forces vertically and horizontally and setting up and solving suitable equations or otherwise verify this value by calculation.

  • Describe what happens to the frictional force, the resultant force and the acceleration
    (i) before this point? (ii) after this point?

• Set µ equal to 0.5 and P equal to 25.

  • Click on the animate button near angle of P to see the effect of increasing the angle while keeping P constant. What do you notice?

  • Explain the behavior of the reaction force R and the Frictional force Fr.

• Set µ equal to 0.5 and P equal to 25.

  • Use the spreadsheet to find the maximum value of the resultant force F as the angle of P varies.

  • By resolving forces vertically and horizontally and setting up and solving suitable equations or otherwise verify this value by calculation.

• You may have noticed that a smaller value of P was needed to break equilibrium when the angle was 50° than when the angle was zero.

  • For µ = 0.5 investigate which angle gives the smallest value of P needed to break equilibrium. Try to justify your results mathematically.

  • Now try to generalize : find in terms of µ formulae for the smallest value of P needed to break equilibrium and the angle that it occurs for.