A 12.0-kg mass. fastened to the end of an aluminium wire with an un stretched length of 0.50 m, is whirled in a vertical circle with a constant angular speed of 120 rev/min. The crosssectional area of the wire is 0.014 cm2. Calculate the elongation of the wire when the mass is (a) at the lowest point of the path and (b) at the highest point of its path.
Solution 89P Step 1: Introduction: In this question, we need to find the elongation the wire When the mass is at the lowest point And when the mass is at the highest point Data given Mass m = 12.0 kg 2 F = mg = 12.0 × 9.8 m/s = 117.6 N Length l 0 0.50 m Angular velocity = 120 rev/min = 120 rev/min × (1/60) × 2 = 12.56 rad/s Area of cross section A = 0.014 cm = 0.014 × 10 m 2 2 Step 2: We shall find the force exerted on the aluminium wire It is given by F w m × × r Here r = l = 0.50 m 0 Substituting values we get F = 12.0 kg × (12.56 rad/s) × 0.50 m w F w 947.48 N 947.5N Here we have the force of the wire as 947.5N