Use mathematical techniques to determine Fnet and acceleration for each of the following forces arrangements. For each, remember to include magnitude, unit, and direction

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Use mathematical techniques to determine Fnet and acceleration for each of the following forces arrangements. For each, remember to include magnitude, unit, and direction

Physics
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|dw:1436166774039:dw|
how can we solve this type of problem can someone plz explain me
\[ \sum F_y = 10N \sin (35^\circ) - 20N \\ \sum F_x = 10N \cos(35^\circ) \]\[ \mathbf F = \mathbf i \sum F_x + \mathbf j\sum F_y \]

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We could also say\[ \sum F_y = 10N\sin(35^\circ) +20N\sin(-90^\circ) \]Since \(\sin(-90^\circ) = -1\).
|dw:1436168731242:dw|
wait but how can we show that on the diagram
like how is it be -90
|dw:1436169653345:dw| angle with the \(x\) axis... clockwise angles are negative
oh ok thnx alot
we can write the subsequent vector equation: \[\Large {{\mathbf{F}}_{\mathbf{1}}} + {{\mathbf{F}}_{\mathbf{2}}} + M{\mathbf{g}} = M{\mathbf{a}}\] where a is the acceleration of our object, and M is its mass, furthermore g, is the earth gravity |dw:1436186357407:dw|
so we have the subsequent scalar equations: \[\Large \left\{ \begin{gathered} {F_1}\cos \theta = M{a_x} \hfill \\ \hfill \\ {F_1}\sin \theta - Mg - {F_2} = M{a_z} \hfill \\ \end{gathered} \right.\] where F_1 and F_2 are the magnitude of the corresponding vectors |dw:1436186583052:dw|

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