Balancing interactivity with springs and weights.
Balance the bar with the three weight on the inside.
Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?
Experimentation is a good preliminary step to get a feel for the dynamics and relationships operating here, before attempting some analysis.
There is also scope for a natural progression into general results.
Students may also develop their own questions with a little encouragement.