A system of two paint buckets connected by a light-weight rope is released from rest with the 12.0-kg bucket 2.00 m above the floor (Fig. P7.51). Use the principle of conservation of energy to find the speed with which this bucket strikes the floor. Ignore friction and the mass of the pulley.

Solution 55P Step 1: T1= 0.5 N T = m g = m a 1 1 1 m 2 T = m a 2 T m g + m g T = m a + m a 1 1 2 2 1 2 m 1 + m g2= m a 1 m a 2 g(m 2 m ) 1 a(m + m2) 1 a = (m m )g/(m + m ) 2 1 2 1 Step 2: The common acceleration of 12 kg bucket downwards and 4 kg bucket upwards is a = (m 2 m )g1(m + m2) 1 2 a = (12 kg 4 kg) 9*81 m/s /(12 kg + 4 kg) 2 a = 4.905 m/s