(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 = 10 ms^{-2})].
(b) A constant force F acts on a toy car of mass 5 kg and increases its velocity from 5 ms(^{-1}) to 9 ms(^{-1}) in 2 seconds. Calculate :
(i) the magnitude of the force ; (ii) velocity of the toy car 3 seconds after attaining a velocity of 9 ms(^{-1}).
Explanation
(a)
From Lami’s theorem,
(frac{T_{1}}{sin 150} = frac{T_{2}}{sin 140} = frac{50}{sin 70})
(T_{1} = frac{50 sin 150}{sin 70})
= (frac{50 times 0.5}{0.9397} = 26.6N)
(T_{2} = frac{50 sin 140}{sin 70})
= (frac{50 times 0.6428}{0.9397} = 34.2N)
The tensions are 26.6N and 34.2N respectively.
(b)(i) Given F = ?, u = 5 ms(^{-1}) ; v = 9 ms(^{-1}) ; t = 2s.
acceleration, (a = frac{v – u}{t})
= (frac{9 – 5}{2} = 2 ms^{-2})
Force, (F = ma = 5 times 2 )
= (10N).
(ii) (v = u + at)
(u = 9 ms^{-1}; a = 2 ms^{-2} ; t = 2s)
(v = 9 + 2(3))
= (9 + 6 = 15 ms^{-1}).