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A system of two paint buckets connected by a light-weight

ISBN: 9780321675460 31

Solution for problem 55P Chapter 7

University Physics | 13th Edition

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Problem 55P

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.

Step-by-Step Solution:

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

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