HETEROGENEOUS IDEAS FOR INTERESTING DISCUSSION II JULIUS SUMNER MILLER El Camino College, El Camino College, California We continue this new adventure with another series of inviting inquiries. 1. Examine the behavior of a body in free fall (near the earths- Discover the following for a body falling from rest : (a) The distances passed over during successive seconds are in the ratio of the successive odd numbers beginning with one. (b) The distances passed over measured from rest are in the ratio of the squares of the successive integers beginning with one. 2. A wheel rolls along a horizontal road. Is there a point which has a velocity straight up or down? 3. A piece of mud leaves the hindmost part of a rolling wheel. Will it hit the wheel again? 4. Monument workers engrave stones by sand-blasting. They first cover the face of the stone with a rubber sheet (^ or so thick) and cut out the letters or design in the rubber. The sand-blasting then cuts out the stone where it is exposed but does not cut away the rubber. Explain this in good physics. 5. Consider a horizontal angle-iron track with one end inclined. On the horizontal track rests an array of billiard balls. If one is taken up the plane and released it rolls down, strikes the system at rest, and one ball rolls away from the far end. We say mv^mv. Now if two are released we find two going away. We say 2mv==2m’u. This is all on the strength of momentum conservation. But why in the second case cannot one go away with a velocity 2v? We would then have 2mv==m(2v). 6. Two men A and B of identical weights hold the ends of a rope which passes over a frictionless pulley. A climbs up. What happens toB? 7. Consider the following problem: A column of troops 3 miles in depth marches along a road. An officer rides at a uniform rate from the rear of the column to the head, and back again at once, reaching the rear of the column just as an advance of 4 miles has been made. How far did the officer ride? A student submits the following solution: ^If 4 miles was advanced by the army while the officer traveled up and back, 2 miles was advanced while the officer traveled up. Therefore, the officer traveled 3 miles+2 miles+3 miles=8 miles.?? Now 8 miles is the correct answer but is the logic of the solution acceptable? It is not uncommon in physics to find answers which are gotten by physically wrong means. 338

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HETEROGENEOUS IDEAS FOR INTERESTINGDISCUSSION II

JULIUS SUMNER MILLEREl Camino College, El Camino College, California

We continue this new adventure with another series of invitinginquiries.

1. Examine the behavior of a body in free fall (near the earths-Discover the following for a body falling from rest :

(a) The distances passed over during successive seconds are in theratio of the successive odd numbers beginning with one.

(b) The distances passed over measured from rest are in the ratioof the squares of the successive integers beginning with one.

2. A wheel rolls along a horizontal road. Is there a point which hasa velocity straight up or down?

3. A piece of mud leaves the hindmost part of a rolling wheel.Will it hit the wheel again?

4. Monument workers engrave stones by sand-blasting. They firstcover the face of the stone with a rubber sheet (^ or so thick) andcut out the letters or design in the rubber. The sand-blasting thencuts out the stone where it is exposed but does not cut away therubber. Explain this in good physics.

5. Consider a horizontal angle-iron track with one end inclined.On the horizontal track rests an array of billiard balls. If one is takenup the plane and released it rolls down, strikes the system at rest,and one ball rolls away from the far end. We say mv^mv. Now iftwo are released we find two going away. We say 2mv==2m’u. This isall on the strength of momentum conservation. But why in thesecond case cannot one go away with a velocity 2v? We would thenhave 2mv==m(2v).

6. Two men A and B of identical weights hold the ends of a ropewhich passes over a frictionless pulley. A climbs up. What happenstoB?

7. Consider the following problem: A column of troops 3 miles indepth marches along a road. An officer rides at a uniform rate from therear of the column to the head, and back again at once, reaching the rear ofthe column just as an advance of 4 miles has been made. How far did theofficer ride? A student submits the following solution: ^If 4 miles wasadvanced by the army while the officer traveled up and back, 2 mileswas advanced while the officer traveled up. Therefore, the officertraveled 3 miles+2 miles+3 miles=8 miles.?? Now 8 miles is thecorrect answer but is the logic of the solution acceptable? It is notuncommon in physics to find answers which are gotten by physicallywrong means.

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