Answer
a) $m = 7.065 kg $
b) $m = 3.947 kg $
Work Step by Step
a) We assume that the pulley is massless. We know that the left mass is 2.1 kg. Thus, we treat this as a system, and we use Newton's second law to find:
$-.64(m+2.1)=2.1gsin60-mgsin20\\ m = 7.065 kg $
b) We use a similar process to find:
$.76(m+2.1)=2.1gsin60-mgsin20\\ m = 3.947 kg $
