Light Weights
This activity provides an interesting context in which to engage with weight, mass and gravitation, and is aimed at A-level students (Key Stage 5).
Detailed teachers' notes for this activity are available on our NRICH website.
Light Weights
The weight $W$ of an object on earth depends on the mass $m$ of
the object and the force of gravity. The weight is
usually given by the expression
$$
W = 9.8 m.
$$
However, the actual weight decreases the further you get from the
centre of the earth. Newton worked out that weight can be measured
more accurately as
Here $M$ is the mass of the earth, $m$ is the mass of the small object you are trying to weigh in $kg$ and $R$ is the distance from the centre of the earth in metres; $W$ is the weight in Newtons, which have units of metres kilograms per second per second.
In Olympic weightlifting the biggest competitors can sometime lift 200kg masses overhead. Sometimes weight lifting events take place in high altitude cities and sometimes at sea-level. The question that you are asked is this:
Does the variation in gravity provide a significant effect for weightlifters?
Something else to think about: How high in an airplane or rocket would you have to go before you could lift a 200kg mass overhead?
NOTES AND BACKGROUND
$G$ is called Newton's gravitational constant, which you can read about on Wikipedia.The universal law of gravitation expressed here gives extremely accurate predictions for the orbits of suns and planets. It is eventually superseded by the difficult theory of general relativity.
$G$ is called Newton's gravitational constant, which you can read about on Wikipedia.The universal law of gravitation expressed here gives extremely accurate predictions for the orbits of suns and planets. It is eventually superseded by the difficult theory of general relativity.
Further information
Detailed teachers' notes for this activity are available on our NRICH website.
