CALC ?You connect a light string to a point on the edge of a uniform vertical disk with radius ?R ?and mass ?M. ?The disk is free to rotate without friction about a stationary horizontal axis through its center. Initially, the disk is at rest with the string connection at the highest point on the disk. You pull the string with a constant horizontal force F until the wheel has made exactly one-quarter revolution about a horizontal axis through its center, and then you let go. (a) Use Eq. (10.20) to find the work done by the string. (b) Use Eq. (6.14) to find the work done by the string. Do you obtain the same result as in part (a)? (c) Find the final angular speed of the disk. (d) Find the maximum tangential acceleration of a point on the disk. (e) Find the maximum radial (centripetal) acceleration of a point on the disk.
Solution 65P Step 1: (a).Work done by the string is = FR cos R W = Fds 0 = FR /2 W = .d 0 /2 W = FR cos 0 /2 W = FR sin 0 W = FR Step 2: (b).Work done by the string is work = 1/2 Iw 2 FR = 1/2(MR /2)w 2 FR = (MR /4)w 2 2 w = 4F/MR w = 4F/MR