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

© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Investigating friction



Why doesn’t the climber slide down the rock?

What forces could be helping to keep her in this position?


What happens as the force of the push is increased?

Push Heavy package

Why will a very small push not move the object?

What factors do you think influence a friction force?

Think about:



The modelling cycle

Defineproblem

Observe

Validate

Analyse

InterpretPredict

Real world Mathematics

Set up a model


Investigating frictionYou need:

Investigate your ideas

wooden block(s)

pulley and clamp

hanger and masses

or elastoscale

books


Horizontal pull, P

Think about:How do you think the friction force, F, varies with an increasing pulling force, P?

Sketch a graph

P0

Think about:How does the shape of the graph alter as the mass of the book is increased?

F


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


Plot a graph showing how limiting friction, FMAX varies with normal contact force, N.

N0

FMAX

Think about: Is FMAX = constant N a good model for friction?


Modelling friction – Summary

F P

P

F ≤ N where F is the friction, N is the normal contact force

and is a constant called the coefficient of friction

P is gradually increased until sliding occurs

Force diagram

N

mg

• F acts tangentially along the two surfaces

• F acts in a direction to oppose motion

• There is a maximum friction force, FMAX

• Before sliding F = Pmaintains equilibrium

• Psliding = FMAX

• When sliding is taking place P FMAX


Modelling friction – Summary

F P

N

mg

Graph of F against P

P0

F

FMAX

Psliding

no sliding- static

sliding- dynamic

When the bodies are not moving F ≤ N

When the bodies are moving F = N


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 Nuffield Free-Standing Mathematics Activity Investigating friction.

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