tutorial sheet 9

# tutorial sheet 9 - an equilibrium point Calculate if the...

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PAP111/PHYS1A Tutorial Sheet 9 19 th of November 2010 Claus-Dieter Ohl 1 1) Angular momentum and Kepler’s law A particle of mass m moves along a straight line with constant speed in the x-direction, a distance b from the x-axis. Does the particle possess any angular momentum about the origin? Explain why the amount of its angular momentum should change or should stay constant. Show that Kepler’s 2 nd law is satisfies by showing that the two shaded triangles in the figure have the same area when t 4 - t 3 = t 2 - t 1 . 2) Gravitational field Three objects of equal mass are located at three corners of a square of edge length l as shown in the figure. a) Find the gravitational field at the fourth corner due to the other three objects. b) Assume the fourth corner is now occupied with an object of mass m , too. What is the gravitational field along the line AB? Show that the center of mass of the 4 mass system is

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Unformatted text preview: an equilibrium point. Calculate if the center of mass is a stable or an unstable equilibrium. c) Without calculation, can you write down the gravitational field at a distance r >> l from the center of mass? Then prove this with a calculation. PAP111/PHYS1A Tutorial Sheet 9 19 th of November 2010 Claus-Dieter Ohl 2 3) Special Relativity A muon formed high in the Earth ’ s atmosphere travels at a speed v = 0.990 c for a distance of 4.60 km before it decays into an electron, a neutrino, and an anti-neutrino (    e       a) For what time interval does the muon live as a measured in its reference frame? b) How far does the Earth travel as measured in the frame of the muon?...
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## This note was uploaded on 12/08/2010 for the course SPMS pap111 taught by Professor Claus-dieterohl during the Fall '10 term at Nanyang Technological University.

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tutorial sheet 9 - an equilibrium point Calculate if the...

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