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
 

$$W =\frac{6.67428 \times 10^{-11}Mm}{R^2} N, \quad M = 5.972 \times 10^{24} \mbox{kg}.$$  
Here $M$ is the mass of the earth, $m$ is the mass of the small object you are trying to weigh in $\mbox{kg}$ 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 $200\mbox{kg}$ 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 $200\mbox{kg}$ mass overhead?