# Mvot mgybot or vot vop 2gytop ybot mv figure 8 42

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Unformatted text preview: sed spring on a frictionless track .~hat turns upward at a 45 angle, as shown in ~ig. 8-43. Find an expression for the horizontal range x shown in the figure, as. a function of the distance d by which the spring is initially compr~ed, the spring constant k, aild the height h ot the ramp. 0 v;op + 4gR (since Ytop- Ybotis the diameter of the circle). The result of part (a) then leads to V~ot S; v;op + 4vrop = 5v;op, equivalent to the assertion in the problem. Problem 68. An.84Q-kg roller-coaster car is launched from a giant spring of constant k = 31 kN/m into a frictionless loop-the-Ioop track of radius 6.2 m, as shown in Fig. 8-44. What is the minimum amount that the spring must be compressed if the car is to stay on the track? Solution The comments made in the solution to the previous problem hold here also, so x = VU9, where point 2 is Solution If the car stays on the track, the radial component of its acceleration is v2/ R, and the normal force is CHAPTER8 tllanzero. Thus, N = mv2/ R + mg cos 8 ~. 0, 'ifgB.coso. Now - cosO has its maximum value ofthe loop (0 = 180), so v~ ~ gR is the for the car to stay on the track an the way :I~t...
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