CP ?A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in Fig. 10.10. The pulley is a uniform disk with mass 10.0 kg and radius 50.0 cm and turns on frictionless bearings. You measure that the stone travels 12.6 m in the first 3.00 s starting from rest. Find (a) the mass of the stone and (b) the tension in the wire.
Solution 14 E Step 1: Data given Mass of pulley M = 10.0 kg Radius R = 50.0 cm Distance travelled d = 12.6 m Time taken t = 3.00 s We shall find the acceleration of the stone down the rope It is obtained using 2 d = ut + 1/2at Here the initial distance u = 0 Hence we have 2 d = (1/2) × at Substitute the values we get 2 12.6 m = (1/2) × a × (3.00 s) Rearrange to find “a” 12.6 m 0.5 ×(3.00) a a = 2.8 m/s 2 Step 2 : Tension of the system is equal to the torque That is = TR = I TR = 1/2(MR ) × (a/R) T = 1/2 (M × a) Substitute the values we get T = 1/2 (10.0 kg × 2.8 m/s ) T = 14 N Hence we have the tension on the string is 14 N