hw13 - TAM212 Introductory Dynamics Spring 2005 S....

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Unformatted text preview: TAM212 Introductory Dynamics Spring 2005 S. Balachandar Homework 13 (2.113, 2.123) 2.113 Work done by gravity = Change in kinetic energy from release to bottom B 12 mgh = mv 2B 2 gh vB = P d* B Let P be a point somewhere on the circular loop. So the work done in pushing the particle from the bottom to the point P is given by W = ∆T 1 −mgd∗ = m(v2 − v2 ) P B 2 1 − gd∗ = (v2 − 2 gh) 2P v 2 = 2 g (h − d ∗ ) P Frn = macN at P when P is at top barely zero 2 mv P  N + mg = ρ 2 g (h − d ∗ ) g= where d∗ = d at top ρ 2(h − d) since ρ = d/2 1= d /2 d = 4h − 4d 5d h= 4 1 Any smaller h and the paricle will not make it to the top. 2.123 ϕ1 = − & ϕ2 GMm re GMm =− 6.61re Work = ϕ1 − ϕ2 GMm 1 =− 1− re 6.61 1 gr2 m 1− =−e re 6.61 = −0.849mgre 2 ...
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hw13 - TAM212 Introductory Dynamics Spring 2005 S....

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