The acceleration of each object will be 2.31 m/s².While the direction for mass 1 is down, mass 2 is left and mass 3 is up.
The tension force is described as the force transferred through a rope, string, or wire as it is pulled by opposing forces.
The tension force is applied along the whole length of the wire, pulling energy equally on both ends.
From Newton's second law, the net force is equal to the product of the mass and acceleration. Forces and tension acting upward are positive while the downward is taken as negative.
Foer mass m₁ only vertical force is considered.
[tex]\rm \sum F_y=ma_y \\\\ + T_{12}-m_1g =-m_1a \\\\ -T_{12}+39.2 \ N=(4.00 \ kg )a[/tex]
For mass m₂ both horizontal and verticle force is considered;
[tex]\rm \sum F_x=ma_x \\\\ -T_{12}+f+T_{23}\\\\ -T_{12}+\mu_kN+T_{23} \\\\ T_{12}-0.350(9.80 \ N)-T_{23}=(1.00 \ kg)a[/tex]
[tex]\rm \sum F_y =ma_y \\\\ N-m_2g=0[/tex]
Foer mass m₃ only vertical force is considered.
[tex]\rm \sum F_y=ma_y \\\\ T{23}-m_2g=+m_3a \\\\ T_{23}-19.6 \ N=(2.00 \ kg)a[/tex]
Adding all the obtained forces we get;
[tex]\rm +39.2 \ N-3.43 \ N-19.6 N=(7.00 \kg) a\\\\ a=2.31 \ m/s^2[/tex]
Hence, the acceleration of each object will be 2.31 m/s².While the direction for mass 1 is down, mass 2 is left and mass 3 is up.
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