Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 6 - Applications of Newton's Laws - Problems and Conceptual Exercises: 44

Answer

$T1 = m1a$ $T2 - T1 = m2a$ $m3g - T2 = m3a$ a = $4.9 m/s^2$

Work Step by Step

By analyzing the forces acting on each block and utilizing Newton's Second Law, we can solve the problem and find the acceleration of the masses. On block ($M1$), there are three forces acting on the block. These are the Normal Force of the table on the block($N$), the force of gravity downward($mg$) and the tension force exerted by the rope connected to the block($T1$). On block m2, there are four forces exerted on the block. These are the Normal Force of the table on the block($N$), the force of gravity downward($mg$), the Tension Force($T2$) in the positive direction and the Tension Force($T1$) in the negative direction. Finally, on block($T3$), there are only two forces acting on the block. These are the force of gravity downward($mg$) and the tension force upward($T2$) Using Newton's Second Law, which states that the net component forces acting on an object equals an object's mass($m$) times acceleration($a$), we can write relations for all three blocks. For block $m1$, $T1$ is the only force acting horizontally on the block, $T1 = m1a$. For block $m2$, $T2$ acts in the positive horizontal direction and $T1$ acts in the negative horizontal direction. As a result, $T2 - T1 = m2a$. For block $m3$, $T2$ acts in the negative direction because the block accelerates downward. $m3g$ then acts upward. As a result, $m3g - T2 = m3a$. By using algebraic manipulation, $T2 = a(m1 + m2)$ and $m3g = (m1 + m2 + m3)a$. Since $m1 = 1 kg$, $m2 = 2kg$, $m3 = 3kg$ and g is $9.8 m/s^2$, $a$ is $4.9m/s^2$.
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