Theory question 114
Statics(a) A body P of mass q kg is suspended by two light inextensible strings AB and DB attached to a horizontal table. The strings are inclined at 30° and 60° respectively to the horizontal and the tension in AB is 48 N. If the system is in equilibrium: (i) sketch a diagram to represent the information; (ii) calculate the tension in DB, (iii) find the value of q. [Take g = 10 ms−2]
(b) A ball is thrown vertically upwards with a velocity of 20 ms−1. Find, correct to two decimal places the: (i) maximum height reached by the ball; (ii) time taken to reach the maximum height. [Take g = 10 ms−2]
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(a)(i) Sketch: B below the support line, BA at 30° and BD at 60° to the horizontal on opposite sides, weight 10q N straight down.
(ii) Horizontally: 48 cos 30° = T cos 60°, so T = 83.14 N.
(iii) Vertically: 48 sin 30° + 83.14 sin 60° = 24 + 72 = 96 = 10q, so q = 9.6.
(b)(i) v² = u² − 2gh: h = 400/20 = 20.00 m.
(ii) t = u/g = 2.00 s.
Resolve the tensions horizontally and vertically.