happens to this energy? ( c ) How much mechanical energy is long during the seco

Question

happens to this energy? ( c ) How much mechanical energy is long during the second bounce? Riding a Loop - the - Loop. A car in an amusement park ride rolls without friction around the track shown in Fig. 7.32. It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. What is the minimum value of h ( in terms of R ) such that the car moves around the loop without falling off at the top ( point B ) ? ( b ) If h = 3.50R and R = 20.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers, when the car is at point C, which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale. A 2.0 - kg piece of wood slides on the surface shown in Figure 7.32 Problem 7.46. Figure 7.33 Problem 7.47.

Explanation / Answer

a) energy conservation: mgh = mg(2R) +mvB2/2 at B, mg = mvB^2/R so,mvB^2/2 = mgR/2 so mgh = mg(2R) + mgR/2 ?h = 2R + R/2 h = 5R/2 b) energy conservation: mgh = mgR +m*vc^2/2 vc = v(2g(h - R)) = v(8gR) = 38.59 m/s c) radial acceleration ar = vc^2/R= 78.37 m/s2

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