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.
(i) before this point? (ii) after this point ?
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 m = 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 m formulae for the smallest value of P needed to break equilibrium and the angle that it occurs for.