Copper cages the magnesium not magnesium caging the copper. The only purpose the copper serves is to prevent the magnesium from falling through the stopper hole. The stopper hole is there to allow gas to displace the solution. If you cover up the stopper hole "you've [potentially] made a bomb", as my professor would always say.
One last time;
1) Roll/curl the
magnesium up - if it's been oxidized use sandpaper to clean
then weight it.
2) Get a
copper wire and twist it around the
magnesium to protect it from falling through the stopper hole. Magnesium will be "chewed up", in a respect, by the HCl and start to break apart. If you lose any material it's experimental error.
3) Make a hook coming out and back in from the side of the stopper and then cap it.
This is not a effective method to calculate rate of a reaction due to product/reactant potential loss.