A stone at the end of a sling is whirled in a vertical circle of radius 1.00 m a

Question

A stone at the end of a sling is whirled in a vertical circle of radius 1.00 m at a constant speed v0 = 2.30 m/s as in Figure P4.57. The center of the string is 1.50 m above the ground. 30.0° 30.01 Figure P4.57 (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 (absolute value) Direction O upward O downward O toward the center of the circle o in the direction of vo (d) What is the acceleration of the stone just after it is released at A? Magnitude (absolute value) Direction O toward the center of the circle o downward O upward o in the direction of Vo

Explanation / Answer

(A) yf - yi = v0y t + ay t^2 /2

  
0 - (1.50 + 1sin30) = 2.30cos30 t - 9.8 t^2 /2

4.9 t^2 - 1.99t - 2 = 0

t = 0.873 sec

range = 2.30 sin30 t = 1 m   

(B) 0 - (1.50 + 1sin30) =- 2.30cos30 t - 9.8 t^2 /2

4.9 t^2 + 1.99t - 2 = 0

t = 0.467 sec

range = 2.30 sin30 t = 0.54 m

(C) a = v0^2 / r = 5.29 m/s^2

toward the center of the circle.

(D)a = v0^2 / r = 5.29 m/s^2

toward the center of the circle.

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