Smugglers. Rumor has it that a company has been smuggling gold out of the country using sealed, cylindrical barrels with hollow walls. They pour molten gold into the hollows, and then fill the remainder of the barrel's internal volume with packing peanuts. The total mass of the gold-walled barrel was designed so that it exactly matches those used to transport a volatile chemical that cannot be exposed to air (and therefore the barrel cannot be opened and checked). The X-ray machine usually used to screen containers is suspiciously damaged and not available. (a) There are 20 barrels total, and they are all identical: mass m= 50.0 kg, height h= 1.2 m, and diameter D = 0.25 m. How do you determine which ones have walls filled with gold (and are essentially hollow on the interior except for packing peanuts) and those completely filled with the volatile chemical (a tightly-packed powder) where the mass is uniformly distributed? Hint: apply the concepts of moment of inertia. Is the moment of inertia of the hollow cylinder less than, greater than or equal to the moment of inertia of the solid cylinder? (b) Assume that, in the case of the gold-filled barrels, the entire mass is concentrated at the outer wall of the barrel and, in the case of the barrels filled with the chemical, the mass is distributed evenly throughout the volume of the cylinder. You can neglect the circular bottoms and the lids of the barrels, and assume there is no slipping. What is the acceleration of the center of mass of each of the barrels as they roll down a 30° inclined plane? (c) How much time does it take each barrel to roll 14.0 m down the 30° plane?
Smugglers. Rumor has it that a company has been smuggling gold out of the country using sealed, cylindrical barrels with hollow walls. They pour molten gold into the hollows, and then fill the remainder of the barrel's internal volume with packing peanuts. The total mass of the gold-walled barrel was designed so that it exactly matches those used to transport a volatile chemical that cannot be exposed to air (and therefore the barrel cannot be opened and checked). The X-ray machine usually used to screen containers is suspiciously damaged and not available. (a) There are 20 barrels total, and they are all identical: mass m= 50.0 kg, height h= 1.2 m, and diameter D = 0.25 m. How do you determine which ones have walls filled with gold (and are essentially hollow on the interior except for packing peanuts) and those completely filled with the volatile chemical (a tightly-packed powder) where the mass is uniformly distributed? Hint: apply the concepts of moment of inertia. Is the moment of inertia of the hollow cylinder less than, greater than or equal to the moment of inertia of the solid cylinder? (b) Assume that, in the case of the gold-filled barrels, the entire mass is concentrated at the outer wall of the barrel and, in the case of the barrels filled with the chemical, the mass is distributed evenly throughout the volume of the cylinder. You can neglect the circular bottoms and the lids of the barrels, and assume there is no slipping. What is the acceleration of the center of mass of each of the barrels as they roll down a 30° inclined plane? (c) How much time does it take each barrel to roll 14.0 m down the 30° plane?
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Smugglers. Rumor has it that a company has been smuggling gold out of the country using sealed, cylindrical barrels with hollow walls.
They pour molten gold into the hollows, and then fill the remainder of the barrel's internal volume with packing peanuts. The total
mass of the gold-walled barrel was designed so that it exactly matches those used to transport a volatile chemical that cannot be
exposed to air (and therefore the barrel cannot be opened and checked). The X-ray machine usually used to screen containers is
suspiciously damaged and not available.
(a) There are 20 barrels total, and they are all identical: mass m= 50.0 kg, height h= 1.2 m, and diameter D = 0.25 m. How do you
determine which ones have walls filled with gold (and are essentially hollow on the interior except for packing peanuts) and those
completely filled with the volatile chemical (a tightly-packed powder) where the mass is uniformly distributed? Hint: apply the
concepts of moment of inertia.
Is the moment of inertia of the hollow cylinder less than, greater than or equal to the moment of inertia of the solid cylinder?
(b) Assume that, in the case of the gold-filled barrels, the entire mass is concentrated at the outer wall of the barrel and, in the case of
the barrels filled with the chemical, the mass is distributed evenly throughout the volume of the cylinder. You can neglect the circular
bottoms and the lids of the barrels, and assume there is no slipping. What is the acceleration of the center of mass of each of the
barrels as they roll down a 30° inclined plane?
(c) How much time does it take each barrel to roll 14.0 m down the 30° plane?
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