Nuffield FreeStanding Mathematics Activity Investigating friction Nuffield Foundation

Nuffield Free-Standing Mathematics Activity Investigating friction © Nuffield Foundation 2011

Investigating friction Why doesn’t the climber slide down the rock? What forces could be helping to keep her in this position? © Nuffield Foundation 2011

Investigating friction Push Heavy package 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? © Nuffield Foundation 2011

The modelling cycle Mathematics Real world Set up a model Observe Define problem Analyse Validate Interpret Predict © Nuffield Foundation 2011

Investigating friction You need: books hanger and masses wooden block(s) pulley and clamp or elastoscale Investigate your ideas © Nuffield Foundation 2011

Horizontal pull, P Think about: How do you think the friction force, F, varies with an increasing pulling force, P? Sketch a graph Think about: How does the shape of the graph alter as the mass of the book is increased? © Nuffield Foundation 2011 F 0 P

This practical apparatus may help your investigation … or use an elastoscale … Mass M Investigate how the maximum friction force, FMAX, varies with the normal contact force, N Vary N by using different masses M © Nuffield Foundation 2011

Plot a graph showing how limiting friction, FMAX varies with normal contact force, N. FMAX 0 N Think about: Is FMAX = constant N a good model for friction? © Nuffield Foundation 2011

Modelling friction – Summary where F is the friction, N is the normal contact force F ≤ m. N and m is a constant called the coefficient of friction P Force diagram P is gradually increased until sliding occurs • F acts tangentially along the two surfaces N • F acts in a direction to oppose motion • Before sliding F = P maintains equilibrium P F • There is a maximum friction force, FMAX • Psliding = FMAX mg © Nuffield Foundation 2011 • When sliding is taking place P FMAX

Modelling friction – Summary N Graph of F against P F mg FMAX no sliding - static sliding - dynamic When the bodies are not moving F ≤ m. N When the bodies are moving F = m. N © Nuffield Foundation 2011 0 Psliding P

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? © Nuffield Foundation 2011