Theory question 115
Dynamics(a) A bucket full of water with a mass of 8 kg is pulled out of a well with a light inextensible rope. Find its acceleration when the tension in the rope is 150 N. [Take g = 10 ms−2]
(b) A mass of 12 kg is acted upon by a force F, changing its speed from 15 ms−1 to 25 ms−1 after covering a distance of 50 m. Find the: (i) value of F; (ii) distance covered when its speed is 35 ms−1
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Model answer
(a) T − mg = ma: 150 − 80 = 8a, a = 8.75 ms⁻² upwards.
(b)(i) 25² = 15² + 2a(50), so a = 4 ms⁻² and F = 12 × 4 = 48 N.
(ii) 35² = 15² + 2(4)s, so s = 1000/8 = 125 m (from where its speed was 15 ms⁻¹).
Explanation
Use v² = u² + 2as when time is not involved.