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(C bD (H eI (J bK (M ^N (P bQ eR (U ^V (Z b[ (\ #] 1_ #e-f #h 1i #k 1l #r )s *~ ) * , * # ) * ) * 5 * # /  #$ /% )' *3 54 )4 #6 18 #>0? #A 1B #D 1E #K )L *W )X *[ )\ * # ) * ) *0 # * 4 * ) *0 * 4 5 * 5 * 5 * ) * ; * ; * ; * 4 * 4 * ; * 9 * 4  *  4 * 4 * ; * 4 * 4 *  4! *" 4# *$ 4% I& *) ;* *- ;. *> ,? *A 3B *\ ;] *b ;c *y ;z *     f g 2 M            0 2    l  l  m   M  O   U  c                 <  >   a . i                    J  c   e +     +       + 0   5 + 8  9   < + t   y + |  ~ c<  @ cD F  H +   `H`* I (ᇈ| h)LPHY 1351 Fall 2001 Fourth Hour Exam 5 December 2001 Possibly useful information: s = si + vi t + (1/2) a t2 ac = v2/r p = m v S F = 0 v = vi + a t W = F s cos q impulse = F Dt S t = 0 v2 = vi2 + 2 a (s - si) W = F s impulse = Dp x = A cos (wt + f) sin q = opp/hyp A B = A B cos q T = 2 / w impulse = F dt A B = AxBx + AyBy + AzBz cos q = adj/hyp W = F s = F s cos q Ptot = p1 + p2 tan q = opp/adj dW = Fx dx t = I a F = m a t = dL/dt Fg = G [M m /r2 ] F12 = F21 W = Fx dx L = I w G = 6.672 x 10-11 N m2 / kg2 fs,max = s n t = r x F T2 = [4 2 / G M ] r3 fk = k n K = (1/2) m v2 L = r x p U = G M m /r2 g = 9.8 m/s2 10 m/s2 W = DK K = (1/2) I w2 Me = 5.98 x 1024 kg Wc = DU q = qi + wi t + (1/2) aa t2 Re = 6.37 x 106 m E = K + U w = wi + a t P = F / A Fs = k x w2 = wi2 + 2 a (q - qi) P = Po + r g h Us = (1/2) k x2 A1 v1 = A2 v2 Ug = m g h = m g y P + (1/2) r v2 + r g y = constant 1  1 1 P1 + (1/2) r v12 + r g y1 = P2 + (1/2) r v22 + r g y2 Xcm = S xi mi = x dm = x r dV M M M 1 atm = 1.013 x 105 Pa 1 1 1 1 Pa = 1 N/m2 Ycm = S yi mi = y dm = y r dV M M M M = S mi = dm = r dV I = S ri2 = r2 dm = r2 r dV A x B = i (AyBz AzBy0 + j (AzBx AzBx) + k (AxBy AyBx) C = A x B; C = A B sin f C is perpendicular to both A and B and the direction of C is determined by the right-hand rule. PHY 1351 Fall 2001 Fourth Hour Exam 5 December 2001 Name: _________________________________  1. A uniform ladder of length L and weight w = 50 N rests against a smooth, frictionless, vertical wall. If the coefficient of static friction between ladder and ground is s = 0.40, find the minimum angle qmin such that the ladder does not slip. (This is Example 12.4 from Serway, page 344).. 2. A 0.50 kg mass connected to a light spring of force constant 20.0 N/m oscillates on a horizontal, frictionless track. (a) Calculate the total energy of the system if the amplitude of the motion is 3.0 cm ( 0.03 m). (b) Calculate the maximum speed of the mass if the amplitude of the motion is 3.0 cm ( 0.03 m). (c) What is the speed of the mass when the displacement is 2.0 cm (0.02 m)? (d) What are the kinetic and potential energies of the system when the displacement is 2.0 cm (0.02 m)? (This is Example 13.5 from Serway, p 369) 3. The orbital radius of a geosynchronous satellite is about 42,000 km. A geosynchronous satellite has a period of 24 hours. Show all your work and calculate the orbital radius of a geosynchronous satellite. (This was done in class). 4. A water hose 2.0 cm or 0.02 m in diamete)r is used to fill a 20.0 liter bucket. If it takes 1.0 m or 60 s to fill the bucket, what is the speed v at which the water leaves the hose? 1 cm3 = 1 mL=0.001 L 1 L = 103 cm3 (This is Example 15.12 from Serway, p 433). Conceptual Questions: 1. Describe qualitatively the motion of a mass-spring system when the mass of the spring is not neglected. 2. What happens to the period of a simple pendulum if the mass of the bob is doubled? 3. Does the escape speed of a rocket depend on its mass? 4.Why don't we put a geosynchronous weather satellite in orbit around the 45th parallel? Wouldn't this be more useful to the United States than such a satellite in orbit around the equator? 5. Does a ship ride higher in the water of an inland lake or in the ocean? 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