Question

Problem 2. (based on Young & Freedman 9.47) A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius .0200 m. A stone of unknown mass is attached to a very light wire that is wrapped around the rim of the pulley. When the system is released from rest, the stone accelerates downward at 5.9 m/s 2 (a) What is the angular acceleration of the pulley? Answer: 295 rad/s 2 (b) Find the torque on the pulley from the wire. Answer: .148 Nm (c) What is the tension in the wire? Answer: 7.38 N (d) Find the mass of the stone. Answer: 1.89 kg I can't find the right answer for (d)

Answer 1

Given

   mass of solid disc m = 2.5 kg, radius r = 0.02 m
mass of stone M= ?

   when stone released from rest , accelerating 5.9 m/s2so the angular acceleration is a = r*alpha ==> alpha = a/r = 5.9/0.02 = 295 rad/s

b)
  
Torque T = I*alpha
   = 0.5*mR^2*alpha
   = 0.5*2.5*0.02^2*295 N
   = 0.1475 Nm
c)tension in the wire = 7.38 N

d)mass of stone M =?

   tension T = Mg ==> M = T/g = 7.38/9.8 kg = 0.753 kg