Theory question 116
Statics(a) A body P of mass 5kg is suspended by two light inextensible strings AP and BP attached to a ceiling. If the strings are inclined at angles 40° and 30° respectively to the downward vertical, find the tension in each of the strings. [Take g = 10ms−1]
(b) A constant force F acts on the toy car of mass 5kg and increases its velocity from 5ms−1 to 9ms−1 in 2 seconds. Calculate the: (i) magnitude of the force; (ii) velocity of the toy car 3 seconds after attaining a velocity of 9ms−1.
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(a) W = 50 N; the angle between the strings is 70°
Horizontal: TAP sin 40° = TBP sin 30°; vertical: TAP cos 40° + TBP cos 30° = 50
(Lami) TAP = 50 sin 30°/sin 70° ≈ 26.6 N
TBP = 50 sin 40°/sin 70° ≈ 34.2 N
(b)(i) a = (9 − 5)/2 = 2 ms−2, F = ma = 5 × 2 = 10 N
(ii) v = 9 + 2 × 3 = 15 ms−1
The string nearer the vertical carries the larger tension.