Mass m_a rests on a smooth horizontal surface,m_b hangs vertically.If m_a=15.0kg and m_b=8.0kg, determine the magnitude of the acceleration of each block.
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To determine the magnitude of the acceleration of each block, we need to apply Newton's second law of motion.
For block A (m_a), the only force acting on it is its weight (mg), where g is the acceleration due to gravity. Since block A is on a smooth horizontal surface, there is no friction acting on it. Therefore, the net force acting on block A is its weight (mg) in the vertical direction.
For block B (m_b), the only force acting on it is the tension in the string. The tension in the string is equal to the weight of block B (m_bg), where g is the acceleration due to gravity.
Since blocks A and B are connected by a string and the system is assumed to be massless, the tension in the string is the same for both blocks.
Let's assume the acceleration of the system is "a", and it acts in the same direction for both blocks.
For block A:
F_net_A = m_a * a
(m_a * g) = m_a * a
For block B:
F_net_B = m_b * a
(m_b * g) - Tension = m_b * a
Since the system is connected by a string, the tension in the string is the same for both blocks. Therefore, we can say that m_b * g is equal to the tension.
Substituting m_b * g for the tension in the equation for block B:
(m_b * g) - (m_b * g) = m_b * a
0 = m_b * a
Since the net force on block B is zero, block B remains in equilibrium and does not accelerate.
Therefore, the magnitude of the acceleration for block A is:
a = g = 9.8 m/s^2 (acceleration due to gravity)
The magnitude of the acceleration for block B is 0 m/s^2, as it remains stationary.
So, the magnitude of the acceleration of each block is 9.8 m/s^2 for block A and 0 m/s^2 for block B.