Making connections
The end of the first term, yes, it's the end here, we break up on next Wednesday,. Anyway, the end of the first term is a good time to do a Mini investigation. Students are ready in terms of skills but not quite when it comes to knowledge, In particular the way to apply what they know to novel situations. Even more difficult is applying knowledge from different topics to the same problem.
What is the relationship between the mass of an arrow and the range, given that it is projected horizontally with the same bow pulled back by the same amount?
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Always good to start with conservation of energy.
Elastic PE of the bow is converted to KE of the arrow, this will be the same for all arrows. KE which equals 1/2 mv2 is also constant so v2 is proportional to 1/m, v is proportional to1/√m. If fired horizontally range =vt. t depends on the height of projection which is constant so range is proportional to 1/√m.
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It's a lot to take in so early in the course, it's not that they don't know the physics it's just the way it's put together. How did I know the answer? I didn't, I just applied what little I know.
I made the same explanation to a group of second years.
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They've learnt to play the game