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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 7 / Problem 55P

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Chapter 7, Problem 55P

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QUESTION:

A system of two paint buckets connected by a lightweight rope is released from rest with the \(12.0-\mathrm{kg}\) bucket \(2.00 \mathrm{~m}\) above the floor (Fig. P7.55). Use the principle of conservation of energy to find the speed with which this bucket strikes the floor. You can ignore friction and the mass of the pulley.

Equation Transcription:

$12.0-kg$

$2.00\ m$

Text Transcription:

12.0-kg

2.00 m

Questions & Answers

QUESTION:

A system of two paint buckets connected by a lightweight rope is released from rest with the \(12.0-\mathrm{kg}\) bucket \(2.00 \mathrm{~m}\) above the floor (Fig. P7.55). Use the principle of conservation of energy to find the speed with which this bucket strikes the floor. You can ignore friction and the mass of the pulley.

Equation Transcription:

$12.0-kg$

$2.00\ m$

Text Transcription:

12.0-kg

2.00 m

ANSWER:

Solution 55P

Step 1:

${T}_{1}=0.5\ N$

${T}_{1}={m}_{1}g={m}_{1}a$

${m}_{2}g-T={m}_{2}a$

${T}_{1}-{m}_{1}g+{m}_{2}g-{T}_{2}={m}_{1}a+{m}_{2}a$

$-{m}_{1}g+{m}_{2}g={m}_{1}a+{m}_{2}a$

$g({m}_{2}-{m}_{1})=a({m}_{2}+{m}_{1})$

$a=({m}_{2}-{m}_{1})g/({m}_{2}+{m}_{1})$

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