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
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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?
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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
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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?
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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
Force diagram
P is gradually increased until
sliding occurs
• F acts tangentially along the two surfaces
• F acts in a direction to oppose motion
N
• Before sliding F = P maintains equilibrium
P
F
• There is a maximum friction force, FMAX
• Psliding = FMAX
mg
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• When sliding is taking place P  FMAX
Modelling friction – Summary
N
Graph of F against P
F
P
F
mg
FMAX
no sliding
- static
sliding
- dynamic
When the bodies are
not moving F ≤ mN
When the bodies are
moving F = mN
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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