Phys105_ps3_2009 - Problem 2 K&K problem 3.4 Problem 3...

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Physics 105 Problem Set 3 Due: Thursday, October 8, 2009, 3 PM to 208 Jadwin. Reading: Turn this in to the Undergraduate Physics Office in Jadwin 208 by 3:00 PM on Thursday. Please NEATLY write your name, the time (9 or 10 AM) and the room (A09 or 103A) of your MWF class on your homework. Problem 1. Consider a solid cone of uniform density, with total mass M . The height of the cone from base to apex is L . Let the origin be the center of the base of the cone and let the positive z -axis be the axis of the cone about which it has rotational invariance. The cross-section of the cone perpendicular to the z -axis is a circle that is of radius R at the base and this radius is a linear function of z that decreases to zero at the apex. (a) What is the location (a 3D vector) of the center of mass of this solid cone? (b) If instead the cone is hollow , with all of the mass concentrated at the surfaces (including the base of the cone), with a uniform surface density (mass per unit area), where is the center of mass of this hollow cone?
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Unformatted text preview: Problem 2. K&K, problem 3.4. Problem 3. K&K, problem 3.6 (as in problem 2, neglect air resistance). The given landing speed is before the tailhook snags the sandbag. Problem 4. K&K problem 3.11. Problem 5. K&K problem 3.14. Assume the flatcar is initially at rest. The precise meaning of the words here can be ambiguous: Assume that the men jump so that after they jump they are moving a speed u relative to the flatcar. One way they can do this is to run at relative speed u along the flatcar and just continue off the end at this relative speed. In case b, the others stand still on the flatcar while each man runs off. Problem 6. K&K problem 3.15. Problem 7. K&K problem 3.20. u is the speed of the exhaust relative to the rocket. The ascent is vertical. Call the time of launch t = 0. The equation as written in the book is confusing about signs: Since dm/dt is really negative, it should instead say-dm/dt = γm is the rate at which mass is expelled. 1...
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