Two blocks connected by a string are pulled across a horizontal surface by a force with magnitude $F$ applied at an angle $=56\mathrm{.}4$ above the horizontal and applied to the rightmost block, as shown in the drawing. The mass of the block on the left is $m_1=1\mathrm{.}23kg,$ and the mass of the block on the right is $m_2=4\mathrm{.}24kg.$ The coefficient of kinetic friction between each block and the surface is $=0\mathrm{.}35,$ the same value for both blocks. The blocks have a common acceleration, $a=2\mathrm{.}87\frac{m}{s^2},$ which is to the right.

Part $($a$)$

Write an expression for the magnitude of the force, $F,$ which is applied to the block with mass $m_2.$ Use variables from the problem statement as well as $g$ for the acceleration due to gravity.

$F=$

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Part $($b$)$

Calculate the magnitude, in newtons, of the applied force $F.$