# How do I find the reactive force of a person pulling a vertical rope?

#### Chemist116

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.​ $\begin{array}{ll} 1.&15N\\ 2.&25N\\ 3.&35N\\ 4.&45N\\ 5.&55N\\ \end{array}$

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?. Last edited:

#### skipjack

Forum Staff
You can write separate equilibrium equations for the platform, the technician, and the pulley just above the technician. You need to assume that the pulleys are frictionless and the cords going round the pulleys have negligible weight.

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#### topsquark

Math Team
You can write separate equilibrium equations for the platform, the technician, and the pulley just above the technician. You need to assume that the pulleys are frictionless and the cords going round the pulleys have negligible weight.
...And the tension on the string is the same at all points on the string.

-Dan

#### skeeter

Math Team
FBD provided ... as stated by skipjack, set up three equations & solve the system.

I get R = 55N

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#### skipjack

Forum Staff
That's what I got, but how come the platform doesn't rotate?

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#### skeeter

Math Team
That's what I got, but how come the platform doesn't rotate?
I wondered about that, also ... torques about the left end where $T_1$ is acting do not balance if one uses a reasonable scale for the platform length.

Chalk it up to a poorly engineered problem.

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#### Chemist116

FBD provided ... as stated by skipjack, set up three equations & solve the system.

I get R = 55N
It seems that's the answer, but I'd like to know what's the conceptual basis for the FBD which you made.

By following your diagram my interpretation from what I can see goes as this.

The first equation I spot is:

$T_{1}=2T_{2}+10$

That was very easy, as is the tension created by the man pulling from the cable.

The second is where I'm confused.

I believe you're referring to:

$T_{2}+R_{pm}=80$

But I don't know why shouldn't I also account for $T_{1}$? Is it because that when you do the analysis for him, $T_{1}$ doesn't intervene? You separate the platform from him as if it doesn't exist. Why?

For something to account in the analysis has to make physical contact? What about the pulley? Doesn't he make contact with the pulley because he is holding a cable which goes across that machine? I'm confused at what's exactly the meaning of the subscript $pm$ Perhaps is person-machine?

I'm understanding that the $R$ appears because he steps with his weight over the machine and the machine responds to him with that reaction. Am I right with this part?

Then for the third equation which I spot might be:

$30+R_{mp}=T_{1}+T_{2}$

But here is where I'm more confused that the earlier. Why exactly shouldn't I consider the guy for the equation?. As in the analysis from above, you seem not to consider him. But, Isn't the machine making contact with him? That machine is also making contact with the $10N$ pulley, it doesn't appear in that equation neither.

I'm also considering that

$R_{mp}=R_{pm}$

Anyways, arranging the equations

I'm getting:

$T_{1}=2T_{2}+10$

$T_{2}+R=80$

$30+R=T_{1}+T_{2}$

Solving this system results into:

$T_{1}+T_{2}+R=2T_{2}+10+80$

$30+R+R=2T_{2}+10+80$

$30+R+R=2 \left( 80-R \right)+10+80$

$4R=60+160$

$R=15+40=55$

By doing this. Is the only thing which makes sense to me at this point guiding myself with your numerical answer, but I'm lost at the considerations to get there. Can you help me to clear out these ideas? :help:

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#### skipjack

Forum Staff
1st equation: pulley in equilibrium
2nd equation: technician in equilibrium (the rope tension and the platform reaction counter the technician's weight)
3rd equation: platform in vertical equilibrium

Nothing is moving, so the vertical forces on each component must sum to zero (i.e. "balance").

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#### DarnItJimImAnEngineer

I think the reason it's confusing is that no one has actually drawn any free-body diagrams yet. I was unable to keep things straight in my head until I had sketched them.

Speaking of reasonable scales, did no one notice that the phone technician weighs 80 newtons? Is this Puss in boots's new vocation, or are we on the moon?

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#### Chemist116

I think the reason it's confusing is that no one has actually drawn any free-body diagrams yet. I was unable to keep things straight in my head until I had sketched them.

Speaking of reasonable scales, did no one notice that the phone technician weighs 80 newtons? Is this Puss in boots's new vocation, or are we on the moon?
Thanks for adding that diagram. However I think my major source of confusion has not been answered yet.

When you do a FDB you do isolate each object right?. But I'm still stuck on how to do this procedure correctly. Which object can be isolated?. The ones making physical contact?. Because if the latter is the case, the third equation doesn't make sense (belonging to the forces affecting the platform where the technician is standing). Where's the weight of the person? I'm only getting a reaction ($R$) pointing downwards? why? Where does that force is coming from? (see the third drawing).

I hope you could help me to clear out my doubts because at this point I'm only learning this as if I'm following a cooking recipe but not learning the mechanical concept of it which is what I'm aiming to. And regarding your comment about reasonable scales. When I first attempted to solve this by my own I didn't noticed it, but you are right. It doesn't make sense, whoever did this problem probably just threw some numbers randomly without considering real world implications, which is odd for a subject devoted to explaining reality. 