CP A skier starts at the top of a very large, frictionless snowball, with a very small initial speed, and skis straight down the side (Fig. P7.55). At what point does she lose contact with the snowball and fly off at a tangent? That is, at the instant she loses contact with the snowball, what angle ? does a radial line from the center of the snowball to the skier make with the vertical?
Solution 63P Step 1 of 3: a) Loses contact implies n 0 y = r 1 y = R cos 2 Step 2 of 3: b) The skier moves in an arc of a circle, so her acceleration is v2 arad = R , directed towards the center of the snow ball. we have F = ya y 2 mv 2 mgcos n = R 2 But n = 0 so her acceleration is a rad = R v = Rg cos…..(1) 2 conservation of energy to get v a2d relation K 1 U + 1 other= K 2 U …2(2) The only force that does work on the skier is gravity, so W = 0 other K 1 0 1 2 K 2 mv2 2 U = mgy = mgR 1 1 U 2 mgy = m2 Rcos The equation (2) becomes mgR = mv + mgR cos 2 2 2 v2= 2gR(1 cos)……………(3) Equate (1) and (3) and find Rgcos = 2gR(1 cos) cos = 2 2 cos 3 cos = 2 2 cos = 3 = 48.2 0