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Answer :
The acceleration of the smaller block is 9.80 m/s².
When the positions of the blocks are reversed, with the 4.00 kg block uphill from the 8.00 kg block, we can calculate the acceleration of the smaller block using the following steps:
1. Determine the net force acting on the system:
o The gravitational force on the larger block (8.00 kg) is [tex](F_{\text{larger}} = m_{\text{larger}} \cdot g).[/tex]
o The gravitational force on the smaller block (4.00 kg) is [tex](F_{\text{smaller}} = m_{\text{smaller}} \cdot g).[/tex]
o The net force is the difference between these forces:
[tex](F_{\text{net}} = F_{\text{larger}} - F_{\text{smaller}}).[/tex]
2. Calculate the acceleration of the smaller block:
o Using Newton’s second law, we have
[tex](F_{\text{net}} = m_{\text{smaller}} \cdot a).[/tex]
o Solving for acceleration:[tex](a = \frac{{F_{\text{net}}}}{{m_{\text{smaller}}}}).[/tex]
Given that the acceleration due to gravity ((g)) is approximately 9.8 m/s², we can compute the acceleration of the smaller block:
[tex][ F_{\text{net}} = m_{\text{larger}} \cdot g - m_{\text{smaller}} \cdot g ][ F_{\text{net}} = (8.00 , \text{kg}) \cdot (9.8 , \text{m/s²}) - (4.00 , \text{kg}) \cdot (9.8 , \text{m/s²}) = 39.2 , \text{N} ][/tex]
[tex][ a = \frac{{F_{\text{net}}}}{{m_{\text{smaller}}}} = \frac{{39.2 , \text{N}}}{{4.00 , \text{kg}}} = 9.80 , \text{m/s²} ][/tex]
Therefore, the acceleration of the smaller block is 9.80 m/s².
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