Problem 1 (10 points): Consider the Atwood's machine shown in the figure below, consisting of three masses and three frictionless pulleys. It can be shown that the acceleration of m is given by a1 g 3m2m3 m1 (4m3 + m2) m2m3m1 (4m3 + m2) M1 M3 m2 a) Through dimensional analyzes show that the expression above has the correct unit. (2 points) b) Find a for the following cases (8 points) 1. m2 = : 0, m = m3, does the result you obtain make sense physically? 2. m2 , m = m3, does the result you obtain make sense physically? 3. m = m3 , does the result you obtain make sense physically ? 4. m2 = 2m1 = 2m3 5. m1 m2, m3 6. m1 m2, M3 7. m2 m1 = m3 8. m1 m2 = m3, does the result you obtain make sense physically?