15. 0/1.25 points | Previous Answers SerPSE7 4.XP.16 My Notes A stone at the end

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15. 0/1.25 points | Previous Answers SerPSE7 4.XP.16 My Notes A stone at the end of a sling is whirled in a vertical circle of radius 1.50 m at a constant speed vo- 1.30 m/s as in the figure. The center of the string is 1.50 m above the ground. (a) What is the range of the stone if it is released when the sling is inclined at 30.0° with the horizontal at A? (b) What is the range of the stone if it is released when the sling is inclined at 30.0° with the horizontal at B (c) What is the acceleration of the stone just before it is released at A? Magnitude xm/s2 Direction O downwand O toward the center of the circle O upward O in the direction of vo (d) What is the acceleration of the stone just after it is released at A? Magnitude m/s2 Direction O downward O toward the center of the circle O in the direction of vo O upward Need Help? Talk toa Tutor

Explanation / Answer

a) total vertical distance it descends = 1.5 + 1.5sin30° = 2.25 m

u = 1.3sin60° upwards = -1.1258 m/s

s = ut + ½at² => 2.25 = -1.1258t + 4.905t² =>

4.905t² - 1.258t - 2.25 = 0 => t = 0.8176 s

range = 1.3cos60°t = .95x.8176 ~= 0.53 m


b) u = 1.3cos30° downwards = 1.1258 m/s

s = ut + ½at² => 2.25 = 1.1258t + 4.905t² =>

4.905t² + 1.1258t - 2.25 = 0 => t = 0.572 s

range = 1.3sin30°t = .65x.5153 ~= 0.372 m

c) radial acceleration = a = v²/r = 1.9²/1.3 = 2.777 m/s² (tangential)

d) after release the object is a projectile and only acceleration is g = 9.81 m/s² vertically downwards

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