S.6 Mechanics Revision Questions1 Caltec S.6

I For a ball bearing falling through a liquid, it has thee forces acting on it namely the up thrust, the weight of the bearing, w and the viscous force F acting as indicated above. As the ball accelerates downwa:ds the velocity V increases conseq:.iently the viscous force F increases. So the sum of the upward forces ie P..-u also increases. But since u and w are constant. it implies that the ball retards. As F increases due to increased veioc1ty an mstant is reached when F"l"u"' w1 anci therefore the acceleration will be zero. Revision Exercise (Mechanics) The velocity of propagation, c, of ripple on the surface of a liquid is given by one of the following equations. i)c2 = ApA./ v iii) c = Ay I •jpA. ii)c = Aply2 iv)c = APvj A. Where A is a dimensionless consistent, 1 is the surface tension of the liquid, p is its densit) and A. is the wavelength of the ripples. aJ use tne mcthoa of aunen..1ons to oetermine which equation 1s correct. b)By a graphical method, use the following figures for water to confirm your choice , and to determine the .alue of A. C(ms·1) 0.67 0.45 0.36 0.27 i..xl0·3(m) l.O j2.2 35 16.1 (coefficient of surface tension of water = 7 .2 x 10·2 Nm-1 and density of water =103 kg:m3) 2 (a){i) Explain the meaning of dimensions of a ph)'sical n1,�nt-itv . , ii)The velocity v of waves of wavelength }., on the surface on the pool of liquid, of surface tension y and density p - ln ?n respectively 1s given by v• =-"-+- where g 1s the2n ).p acceleration due to gravity. Show that the above equation ;s dirr.e:-isionally correct. 1ii)A sphere of radius, a, moving through a liquid of density p with a …