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The farmer and the donkey

Page history last edited by apeel@... 5 years, 4 months ago

4.1.2.P7

 

An old Yiddish joke is told about a farmer in Chelm, a town famous for the lack of wisdom of its inhabitants. One day the farmer was going to the mill to have a bag of wheat ground into flour. He was riding to the mill on his donkey, with the sack of wheat thrown over the donkey's back behind him. On his way, he met a friend. His friend chastised him. "Look at you! You must weigh 200 pounds and that sack of flour must weigh 100. That's a very small donkey! Together, you're too much weight for him to carry!" On his way to the mill the farmer thought about what his friend had said. On his way home, he passed his friend again, confident that this time the friend would be satisfied. The farmer still rode the donkey, but this time he carried the 100 pound bag of flour on his own shoulder!

 

Our common sense and intuitions seem to suggest that it doesn't matter how you arrange things, they'll weigh the same. Let's be certain that the Newtonian framework we are developing yields our intuitive result. Analyze the problem by considering the following simplified picture: two blocks resting on a scale. One block weighs 10 N, the other 25 N. In case 1 the blocks are arranged on the scale as shown in the figure on the left In case 2 the blocks are arranged as shown on the right. Each system has come to rest. Analyze the forces on the blocks and on the scale in the two cases by isolating the three objects -- each block and the scale -- and using Newton's laws and free body diagrams, show that according to the principles of Newton's laws, the total force exerted on the scale by both blocks together must be the same in both cases. (Note: It's not enough to say: "They have to be the same." That's just restating your intuition. We need to see that reasoning using only the principles of our Newtonian framework leads to the same conclusion.)

 

 

Joe Redish 9/27/05

Alan Peel 2/15/15

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