301 (F98) Exam #3

301 (F98) Exam #3 - Physics 301 (Fall 1998) Third Exam...

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Physics 301 (Fall 1998) Third Exam (October 30, 1998) Name 1. [20 points] A particle of mass m is dropped into a hole drilled straight through the center of the Earth. Neglect rotational effects, assume that the Earth is perfectly spherical and has uniform density ρ , and assume that there is no friction with the walls. A. Show that the particle experiences simple harmonic motion about the center of the Earth. B. Find the time required for the particle to return to the opening where it was dropped. Show your work.
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2. [15 points] An alien space craft fires a projectile of mass m directly toward the Earth from a location that is a distance D from the center of the Earth, where D >> R E . The projectile leaves the cannon at velocity v o (relative to the Earth) and picks up speed as it falls to the Earth. Find the speed of the projectile just before it strikes the surface of the Earth. Show your work.
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3. [25 points] A rigid rod of length L and negligible mass is used to attach a small ball of mass m to a
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301 (F98) Exam #3 - Physics 301 (Fall 1998) Third Exam...

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