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24. A child is on a swing whose 3.2-m-Iong chains make a maximum angle of 500 with the vertical. What is the child's maximum speed? ~4e plane? C;~sumeno change in gravitational potential
)i;y,Kinitial Solution
This is precisely the situation described in Example 8-6(a). Thus, V = J2g(1 - cas 00) = V2(9.8 m/s2)(3.2 m)(lcos 50) = 4.73 m/s . == ~mv2 = Ufinal = ~kX2, or V = thx. Thus, 11 = J(40,OOO N/m)/(lO,OOO kg) x . CJ:llJ = 50 m/s. Problem
t;Aspring of constant k, compressed a distance x, is '{lise<! to launch a mass m up a frictionless slope {that makes an angle 0 with the horizontal. Find ran expression for the maximum distance along the ; ;slope that the mass moves after leaving the spring. 25. With x - xo = h and a = g, Equation 2-11 gives the speed of an object thrown downward with initial speed Voafter it has dropped a distance h: v = JV5 + 2gh. Use conservation of energy to derive the same result. 128 CHAPTER 8 Solution
Gravity is a conservative force, so for free fall near the Earth's...

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