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We recently tried this Flubber recipe with the kids at the "Science in the Park" event put on by Rhythms of Grace Homeschool Group. We had so much fun coloring it and getting our hands all squishy...
Build the catapult in different sizes, or with different rubber bands, or pencils of different length - discuss the changes each variable makes to the resultant motion of the projectile. Demonstrate circular motion and rotational KE. Based on the relevant principles, have the kids design and build other working models of catapults. Here are some ideas.