CP ?For the situation described in part (a) of Example 14.5, what should be the value of the putty mass ?m ?so that the amplitude after the collision is one-half the original amplitude? For this value of ?m?, what fraction of the original mechanical energy is converted into heat?

Solution 29E Step 1: a) the equation for the new amplitude, A 2 A 1 M+m Where, A - initial amplitude 1 M - Mass of the block m - Mass of the putty If, the new amplitude, A = A /2 2 1 Then, we can write, A1 M 2 = A1 M+m Cancel out the term A on both sides, 1 1 M 2 = M+m Squaring both sides, ¼ = M / (M+m) Or, (M+m) = 4M Or, m = 4M - M = 3M The mass of the putty should be, 3 times larger than that of the block