In 1980, over San Francisco Bay, a large yo-yo was released from a crane. The 11
ID: 1968866 • Letter: I
Question
In 1980, over San Francisco Bay, a large yo-yo was released from a crane. The 116 kg yo-yo consisted of two uniform disks of radius 32 cm connected by an axle of radius 3.2 an. What was the magnitude of the acceleration of the yo-yo during (a) its fall and (b) its rise? (c) What was the tension in the cord on which it rolled? (d) Was that tension near the cord's limit of 52 kN? Suppose you build a scaled-up version of the yo-yo (same shape and materials but larger) (e) Will the magnitude of your yo-yo's acceleration as it falls be greater than, less than, or the same as that of the San Francisco yo-yo?' (f) How about the tension in the cord?Explanation / Answer
a) the formula a = -g / (1+0.5(R/Ro)^2) .....................(1) Given R0 = 0.032m Here it is in the free fall so the negative sign indicatesthe body is in the free fall. Here we take if the body is moving upwards it takes is positive. So the magnitude of the acceleration is a = g / (1+0.5(R/Ro)^2) Here R = 0.30m R0= 0.032m g = 9.8m/s2 a = 9.8 / [ 1 + 0.5 (0.3/0.032)^2 ] = 0.218 m/sec^2 b) During rise it will be - 0.218 m/sec^2 c)We know the formula T - Mg = Ma T = M(g + a) = 131*(9.8-0.218) =1255.242 N