# Find reactive force at equilbrirm of a person pulling a vertical rope around pulley?

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?.

• I don't see your efforts to solve the issue. – Cesareo Nov 19 '19 at 9:55

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 $$R=55$$.

• what's exactly $P_{r}$?. The weight of the person?. and $P_{l}$ the weight of the platform?. Why the first equation has that way?. I'm stuck at the justification for each equation. Can you help me with that part?. – Chris Steinbeck Bell Nov 10 '19 at 5:01
• Please refer to the added diagram. – Quanto Nov 10 '19 at 6:00
• Thanks but can you explain what do the letters mean?. I'm assuming $R$ means the reaction, $P_r$ the force excerted by the person?. and $P_l$ the force excerted by the platform?. I'm confused if the little $r$ means person or perhaps the rope?. – Chris Steinbeck Bell Nov 11 '19 at 9:18
• My major source of confusion is why the equation for the person eliminates $P_{l}$? Is it because he doesn't make contact with that cable?. Then I'm confused about the reaction. The first $R$ makes sense, the guy steps into the platform with his weight and the platform responds to him with a reaction $R$. But for the platform, isn't the guy making contact with it?. Shouldn't we consider also the weight of the guy for your second equation?. What's the second $R$, why that second $R$ is pointing downwards?. Is it because is the reaction from the platform? – Chris Steinbeck Bell Nov 11 '19 at 9:22
• Is it that the second $R$ is caused by the action the two wires which you named $P_l$ and $P_r$ excert on the platform? or is it because of the guy?. Can you clear out these ideas please?. – Chris Steinbeck Bell Nov 11 '19 at 9:25