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ME208_Fall2010_MT2_Solutions

# ME208_Fall2010_MT2_Solutions - θ& φ& sin φ e θ r...

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ME 208 DYNAMICS ( Section 1 , R. Soylu ) SECOND MIDTERM EXAMINATION January 3, 2011 List Number : Name : Surname : ATTENTION Closed book and notes. Time allowed : 120 minutes Number of questions : 4 ( not equally weighted ) Good Luck Signature : Question 1 ( 15 points ) Question 2 ( 25 points ) Question 3 ( 25 points ) Question 4 ( 35 points ) Total ( 100 points ) Useful formulae Given on the back of this page.

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USEFUL FORMULAE : v = ds dt a = dv dt = 2 2 d s dt v dv = a ds v r = dr dt r a r = dv dt r = 2 2 d r dt r v = v 0 + a c t s = s 0 + v 0 t + 1 2 a c t 2 v 2 = v 0 2 + 2a c (s – s 0 ) v r = v t e r ; v = ρ β & a r = a t t e r + a n n e r a t = v & = s && a n = v β & = ρ β & 2 = 2 v ρ t e r & = β & n e r 3 2 2 2 2 dy 1 dx d y dx   +     ρ = r r = r r e r v r = r & r e r + r θ & e θ r a r = ( r && - r θ & 2 ) r e r + ( r θ && + 2 r & θ & ) e θ r r e r & = θ & e θ r e θ r & = - θ & r e r v r = ( R & ) R e r + ( R θ & cos φ ) e θ r + ( R φ & ) e φ r a r = ( R && - R φ & 2 - R θ & 2 cos 2 φ ) R e r + ( cos R φ d dt (R 2 θ & ) – 2R

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Unformatted text preview: θ & φ & sin φ ) e θ r + ( 1 R d dt (R 2 φ & ) + R θ & 2 sin φ cos φ ) e φ r f ≤ μ N dU = F r • d r r P = F r • v r F ∑ r = m a r ' 1 2 U-= Δ T + Δ V g + Δ V e T = 1 2 mv 2 ; V g = mgh ; V e = 1 2 kx 2 ( ) 2 1 t t t t F dt = = ∑ ∫ r = 2 G r- 1 G r G r = m v r ( ) 2 1 t t O t t M dt = = ∑ ∫ r = 2 O H r- 1 O H r O H r = r r × G r A v r = B v r + ω r × A/ B r r A a r = B a r + ω r × ( ω r × A/ B r r ) + α r × A/ B r r XY dV dt       r = xy dV dt       r + ω r × V r A v r = P v r + rel v r A a r = P a r + 2 ω r × rel v r + rel a r xy dV dt       r = V & x i r + V & y j r...
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