1)Calculate the speed of the car at point A . 2)On the figure of the car, draw a

Question

1)Calculate the speed of the car at point A.

2)On the figure of the car, draw and label vectors to represent the forces on the car at point A.

3)Calculate the magnitude of the force of the track on the car at point A.

4)In order to stop the car at point A, some friction must be introduced. Calculate the work that must be done by the friction force in order to stop the car at point A.

5)Explain how to modify the track design to cause the car to lose contact with the track at point A before desending down the track. Justify your answer.

Explanation / Answer

(a). KE, K = 0.5mv2 =0.5x0.5(1.5)^2 = 0.5625 J Change in gravitaional potential energy, U = mg(h1 - h2)                                                                 = 0.5 x 9.8 x 0.1 = 0.49 J Total energy E = K + U = 0.5625 + 0.49 = 1.0525J                At A, E = K =0.5mv2 Hence, v2 = 2E/m = 2 x 1.0525 / 05 = 4.21 J Therefore, speed, v = 4.21 = 2.052 m/s b) At a there are two forces are acts on the car and they are     1. mg down wards and     2. centripetal force mv^2/2 to upwords C) F on the car exerted by the tract,                      F = mg - m.v2/r = m ( g - v^2/r)                    = 0.5 [ 9.8 - (4.21)^2/0.95 ]                          = 2.68 N (d) W = K = 0.5 m.v2 = E = 1.0525 J (e) To loose contact at A, the centrifugal force > weightof the car                 m.v2/r >mg                   v2/r > g                    v2 > r.g = 0.95x9.8 = 9.31m/s2 That is , speed, v > 9.31 = 3.05 m/s

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