You have got a summer job at CERN, which will test its new particle accelerator. The...

 

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You have got a summer job at CERN, which will test its new particle accelerator. The risk is (according to Some On the Internet) that starting the accelerator results in the formation of a black hole, and your job is to monitor so that the gravity acceleration does not change during startup. The method used is to allow a cylindrical ring with the inner diameter di and the outer diameter dy to roll without sliding down an inclined plane. The cylinder starts from rest at t = 0. It is incredibly important that you can monitor so that the advanced measuring instruments capture the right time at the start and end of the course, but for some reason you do not have to watch the movement itself. A new attempt is about to start, and you start to get thirsty for a cup of coffee. Can you go to the coffeemaker (20 seconds), get your coffee (20 seconds) and come back (20 seconds) while the cylinder is rolling? If yes: how much margin do you have? If no: by how much did you miss? The inclined plane has the angle o = 1° and the length e = 175 m. The cylinder has the inner diameter di = 58 mm, outer diameter dy = 60 mm. The material in the cylinder is a bronze alloy with density p = 8.73 (g/cm3). The friction number between plane and cylinder is large enough to prevent slipping. Line 1: The mass moment of inertia of a two-dimensional body = density x moment of inertia Line 2: Conjugate Rule: (a + b) (a - b) = a2- b2 use g=10 m/s You have got a summer job at CERN, which will test its new particle accelerator. The risk is (according to Some On the Internet) that starting the accelerator results in the formation of a black hole, and your job is to monitor so that the gravity acceleration does not change during startup. The method used is to allow a cylindrical ring with the inner diameter di and the outer diameter dy to roll without sliding down an inclined plane. The cylinder starts from rest at t = 0. It is incredibly important that you can monitor so that the advanced measuring instruments capture the right time at the start and end of the course, but for some reason you do not have to watch the movement itself. A new attempt is about to start, and you start to get thirsty for a cup of coffee. Can you go to the coffeemaker (20 seconds), get your coffee (20 seconds) and come back (20 seconds) while the cylinder is rolling? If yes: how much margin do you have? If no: by how much did you miss? The inclined plane has the angle o = 1° and the length e = 175 m. The cylinder has the inner diameter di = 58 mm, outer diameter dy = 60 mm. The material in the cylinder is a bronze alloy with density p = 8.73 (g/cm3). The friction number between plane and cylinder is large enough to prevent slipping. Line 1: The mass moment of inertia of a two-dimensional body = density x moment of inertia Line 2: Conjugate Rule: (a + b) (a - b) = a2- b2 use g=10 m/s