The tension in the cable between the blocks, T₂, is [tex]\frac{2T_i}{7}[/tex]
The given parameters:
- Mass of the first block, = 2 kg
- Mass of the second block, = 5 kg
The net force on the block system is calculated by applying Newton's second law of motion as follows;
Total mass of the block-system = 2 kg + 5 kg = 7 kg
The acceleration of the block-system;
[tex]a = \frac{T_i}{7}[/tex]
The tension in the cable between the blocks, T₂, is calculated as;
[tex]T_2 = m_2 a\\\\T_2 = 2a\\\\T_2 = 2 \times \frac{T_i}{7} \\\\T_2 = \frac{2T_i}{7}[/tex]
Thus, the tension in the cable between the blocks, T₂, is [tex]\frac{2T_i}{7}[/tex].
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