(a) A bucket full of water with a mass of 8kg is pulled out of a well with a light inextensible rope. Find its acceleration when tha tension in the rope is 150N. [Take (g = 10ms^{-2})].
(b) A mass of 12kg is acted upon by a force F, changing its speed from 15 m/s to 25 m/s after covering a distance of 50m. Find the :
(i) value of F ; (ii) distance covered when its speed is 35 m/s.
Explanation
(a)
Let T be the tension in the rope and W the weight of the bucket of water.
T – W = net force = ma
(T – mg = ma)
(150 – 80 = 8a)
(a = frac{70}{8} = 8.75 m/s^{2}).
(b) m = 12kg ; u = 15 m/s.
v = 25 m/s ; s = 50m ; a = ?
(v^{2} = u^{2} + 2as)
(625 = 225 + 100a implies 100a = 400)
(a = 4m/s^{2})
(t = ?)
(s = ut + frac{1}{2} at^{2})
(50 = 15t + frac{1}{2}(4t^{2}))
(50 = 15t + 2t^{2} implies 2t^{2} + 15t – 50 = 0)
(2t^{2} + 20t – 5t – 50 = 0)
(2t(t + 10) – 5(t + 10) = 0 implies (t + 10)(2t – 5) = 0)
(t = frac{5}{2}s text{or t = -10s})
Since time cannot be negative, t = 2.5 seconds.
(F = mfrac{(v – u)}{t})
= (12(frac{25 – 15}{2.5}))
= (48N)
(2as = v^{2} – u^{2})
(2as = 35^{2} – 15^{2})
(2(4)(s) = 1000)
(s = 125m)