Chapter_8__Problems-1

# Chapter_8__Problems-1 - Problem 8 In Figure 8-32 a...

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Problem 8-? In Figure 8-32, a frictionless roller coaster car of mass m = 825 kg tops the first hill with speed v 0 = 17.0 m/s at height h = 42.0 m. What is its speed at points A, B, and C? E 0 = E A = E B = E C U 0 + K 0 = U A + K A = U B + K B = U C + K C U 0 + K 0 = mgh + ½ mv 0 2 = (825)(9.8)(42.0) + ½ (825)(17.0) 2 U 0 + K 0 = 4.59 x 10 5 J U A + K A = 4.59 x 10 5 J mgh + ½ mv A 2 = 4.59 x 10 5 J v A = 17.0 m/s U B + K B = 4.59 x 10 5 J mgh/2 + ½ mv B 2 = 4.59 x 10 5 J v B = 26.0 m/s U C + K C = 4.59 x 10 5 J 0 + ½ mv C 2 = 4.59 x 10 5 J v C = 33.4 m/s

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Problem 8-23 23 The string in Figure 8-38 is L = 120 cm long, has a ball attached to one end, and is fixed at its other end. The distance d from the fixed end to a fixed peg at point P is 75.0 cm. When the initially stationary ball is released with the string horizontal as shown, it will swing along the dashed arc. What is its speed when it reaches (a) its lowest point and (b) its highest point after the string catches on the peg? v A v B E 0 = E A = E B E 0 = mgL E A = ½ mv A 2 E B = ½ mv B 2 + mg2r 2r = 2(L –d) 2r = 2(1.20 –.75) 2r = .90 m ½ mv A 2 = mgL v A = (2gL) 1/2 v A = [(2(9.8)(1.20)] 1/2 v A = 4.85 m/s ½ mv B 2 = mgL – mg2r v B = [2g(L-2r)] 1/2 v B = [(2(9.8)(.30)] 1/2 v B = 2.42 m/s
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