Nuffield Free-Standing Mathematics Activity Investigating friction

Investigating friction Why doesn’t the climber slide down the rock? What forces could be helping to keep her in this position?

Investigating friction Heavy package Push Think about: Why will a very small push not move the object? What happens as the force of the push is increased? What factors do you think influence a friction force?

The modelling cycle Real world Mathematics Set up a model Observe Define problem Observe Analyse Validate Interpret Predict

Investigating friction You need: hanger and masses wooden block(s) pulley and clamp books or elastoscale Investigate your ideas

Horizontal pull, P Think about: How do you think the friction force, F, varies with an increasing pulling force, P? F Sketch a graph Think about: How does the shape of the graph alter as the mass of the book is increased? P

This practical apparatus may help your investigation Mass M … or use an elastoscale … Investigate how the maximum friction force, FMAX, varies with the normal contact force, N Vary N by using different masses M

Is FMAX = constant  N a good model for friction? Plot a graph showing how limiting friction, FMAX varies with normal contact force, N. FMAX N Think about: Is FMAX = constant  N a good model for friction?

Modelling friction – Summary F ≤ mN where F is the friction, N is the normal contact force and m is a constant called the coefficient of friction P P is gradually increased until sliding occurs Force diagram F acts tangentially along the two surfaces N mg F acts in a direction to oppose motion Before sliding F = P maintains equilibrium F P There is a maximum friction force, FMAX Psliding = FMAX When sliding is taking place P  FMAX

Modelling friction – Summary P N mg Graph of F against P P F no sliding sliding - static - dynamic FMAX When the bodies are not moving F ≤ mN When the bodies are moving F = mN Psliding

Reflect on your work Think about how friction is used in everyday life. For example, could you walk if there were no friction force? Would your shoelaces stay tied up? Could you carry something on a tray if there were no friction? Can you suggest how friction could be increased or decreased in any of the examples? If you had graphs of FMAX plotted against N for different pairs of materials in contact, how could you tell which combination of materials had the highest coefficient of friction?