Different graphs, same effect
What the activity is for
Both the force acting on an object and the time for which it is exerted contribute to the change in momentum: they are compensated quantities.
Here you can show that compensated relationship in a pair of physical artefacts.
What to prepare
- two toy crossbows, one rigged with strong elastic, the other with much weaker elastic, both firing the same bolt
- a wooden block to be (just) knocked over when hit by the bolt
- images of compound bows and longbows (optional)
What happens during this activity
Compare the two crossbows, drawing attention to the force exerted by the elastic. Start with the crossbow with the stronger elastic and show just how much you need to stretch the elastic to fire a bolt that will just knock down the block. (A good everyday synonym for momentum is the
punch that the object can deliver.) The longer the elastic is in contact with the bolt, the greater the duration of the action of the force. You could take this opportunity to reinforce the action of the force on the bolt, to further undermine any residual beliefs that the force is somehow
transferred to the bolt.
Now the compensating focus:
Teacher: Now, who can tell me how far I'll have to pull back the weaker elastic on this bow to increase the momentum of the bolt by the same amount, to deliver the same
punch to the block, just knocking it over again?
You'll have practised beforehand, so that you don't need to lose the flow by too much fiddling whilst experimenting to show what you want clearly. Nevertheless, a few trials are more persuasive that getting it right first time. It also allows more opportunity for discussion, to bring out the compensation between force and time. Students might be encouraged to sketch out force–time graphs to support their reasoning.
You might also show one or more of the interactives from the Physics Narrative to complement the physical contrast you've shown.