The problem is as follows:
The figure from below describes a machine where a phone technician whose weight is $80N$ is standing over a flat platform which has a $30N$ of weight. If the system depicted is at equilibrium and the pulleys supporting the platform are of $10N$ each. Find the reaction modulus of the platform over the person.
$\begin{array}{ll} 1.&15N\\ 2.&25N\\ 3.&35N\\ 4.&45N\\ 4.&55N\\ \end{array}$
This particular problem has left me confused at where should I put the vectors to find the reactive force. I'm assuming that the pulleys in the top are held to a fixed support i.e a wall, therefore its weight will not make part of the analysis.
But to me the problem is what to do with the reaction?. How can I find it?. I presume it is pointing upwards, but what it confuses me is how should I understand the situation where the man is pulling through the cable which is connected to the platform which serves as the base for him to stand.
Can somebody help me here?.
I attempted to put the vectors as indicated in the drawing from below. But I don't know how to go from there?.
Set up the equilibrium equations for the man, the platform and the pulley,
$$P_r + R = 80$$ $$P_l+P_r = 30 + R$$ $$ P_l = 2P_r + 10$$
where $P_l$ and $P_r$ are the left and right pulley pulls. Solve for the reaction to obtain $R=55$.