Pole vaulting
Consider the mechanics of pole vaulting
Age
16 to 18
Challenge level
Problem
The pole vault event consists of these phases:
1. The vaulter stands at the end of the runway holding the pole vertically.
2. The runner sprints along the runway as the top of the pole is moved towards the ground.
3. The pole is planted in the box.
4. The pole flexes and absorbs the energy of the runner.
5. The pole straightens and the runner is propelled up and (hopefully!) over the bar.
This is a fascinating mechanical process!
Can you draw a sequence of simple pictures which represent the stages of a pole vault?
Then consider these questions, using appropriate data for the athlete:
1. What is the locus of the centre of mass of the athlete during this process?
2. How much kinetic energy does the runner and pole contain just prior to planting in the box?
3. How efficiently is this converted into potential energy?
There are various levels of sophistication at which this can be considered - analyse with as much depth as you feel is relevant and you can use real data (some are provided below) or approximations. Either is fine, provided that your assumptions and estimations are clearly stated.
NOTES AND BACKGROUND
You might wish to use the following data:
Pole vaulting world record holders as of January 2011:
Male = 6.14m (Sergey Bubka), Female = 5.06m (Yelena Isinbayeva)
Lengths of poles vary between 2.3m to 6.4m, with weight rated individually
Height and weight of vaulters: Sergey Bubka 1.83m/80kg, Yelena Isinbayeva 1.74m/65kg
Length of runway: 40m
You might wish to use the following data:
Pole vaulting world record holders as of January 2011:
Male = 6.14m (Sergey Bubka), Female = 5.06m (Yelena Isinbayeva)
Lengths of poles vary between 2.3m to 6.4m, with weight rated individually
Height and weight of vaulters: Sergey Bubka 1.83m/80kg, Yelena Isinbayeva 1.74m/65kg
Length of runway: 40m
Student Solutions
This investigative task can be approached at various levels, and there is no specific 'solution' as such.
Teachers' Resources
Why do this problem?
This problem provides an interesting context in which to
engage with centres of mass, potential energy and kinetic energy.
This problem is a good group task and provides a meaningful end of
mechanics module review of ideas or preparatory work for a new
mechanics module. It will be reasonably straightforward for
students to work on in a reasonably unstructured fashion and might,
therefore, be appropriate to set as cover work or for an end of
term activity.
Possible approach
Simply pose the problem and leave students to work on the task
in small groups. As a focus for a lesson ask groups to prepare a
poster describing their answers to the three questions. Should you
wish, as a follow-up task you could as a class discuss the
differences which have arisen and try to determine a collective
'best' answer to the problem. If you are feeling adventurous then
you might wish to talk to the PE department about the physics of
pole vaulting or use digital technologies to attempt to trace
accurately the locus of a pole-vaulter as he or she makes a jump -
the context allows for varying depths of approach.
Possible variation
It will be easy to adapt this task to other sports: high
jumping, long jumping and diving, for example.
Key points of note
The complexity of the modelling assumptions required in this
problem is greater than the mathematics required to solve the
problem at its simplest level - this problem is not looking for a
sophisticated algebraic analysis in the first instance.
As a teacher you are not expected to know the answer to all
questions which might arise during the course of the exploration,
particularly since many will be cross-curricular in nature; you can
use your skills to help students to steer a path through the
problem and to coordinate and maximise the learning potential of
any resulting discussion.