A window cleaner holding his platform up with a rope and pulley

[PAULLIM]

Homework Statement

A window-cleaner of mass 75 kg sits in a cradle of mass 15 kg. The cradle is suspended by a light rope PQ passing over a light frictionless pulley hung by a rope R from a fixed beam on a high building, as shown in the diagram. The cleaner pulls the rope with a force such that the cradle and the cleaner remains stationary. The tension in rope PQ = ?

Relevant Equations

Newton‘s Laws

The answer is 441N instead of 883N, but why? can anyone help?

 

[PeroK]

It would be good to see the diagram.

That said, this question comes up quite often. Tension is a two-way force in an elastic material. To have a tension $T$ in a rope, you need a force equal to $T$ at both ends of the rope. If you only have a force at one end, then the rope accelerates and has effectively no tension.

 

[PhDeezNutz]

I haven't seen your work so I don't know where you are stumbling but here's my guess.

There are 3 forces acting on the cradle(T,N,Mg). And 3 forces acting on the person (T,N,mg). You might think that just because the person is pulling that the tension is not acting on them....but the Tension is a reaction force and what does newtons 3rd law say?

 

[PeroK]

Some diagrams:

Case 1: static equilibrium: a rope is pulled at both ends with a force of magntitude $F$. The tension in the rope is $F$.
$$F \ \leftarrow --------\leftarrow (T = F) \rightarrow ------- \rightarrow \ F$$
Case 2: a rope is pulled at one end with a force of magntitude $T$. The rope accelerates to the right and there is negligible tension in the rope.
$$ --------\leftarrow (T \approx 0) \rightarrow ------- \rightarrow \ F$$
A better analysis of the second case would involve the mass of the rope and a tension that reduces from right to left from $F$ to $0$.
$$ -\leftarrow (T = 0) \rightarrow-------\leftarrow (T = F/2) \rightarrow ------\leftarrow (T = F) \rightarrow - \rightarrow \ F (a = F/m)$$

 

[erobz]

Alternatively, take the free body such that it encapsulates man, the cradle, and severs the rope on each side of the pulley. Given that choice, the normal force of the chair on the man $N$ becomes internal...not relevant here.

 

[kuruman]

And here is (yet) another way to think about this. Look at the figure below left. A screen hides what's below the pulley which is and remains at rest.. If I told you that equal masses $m$ are tied to the two ends of the string, you would say that the tension in each side of the string is $T_1=mg$ and that the string that supports the pulley at its axis would add up to the total weight $T=2T_1=2mg.$

Now I remove the screen to show you what's really behind it (figure right). Would the balance of tensions change simply because I misinformed you about what's behind the screen?

 

[Elj]

Homework Statement: A window-cleaner of mass 75 kg sits in a cradle of mass 15 kg. The cradle is suspended by a light rope PQ passing over a light frictionless pulley hung by a rope R from a fixed beam on a high building, as shown in the diagram. The cleaner pulls the rope with a force such that the cradle and the cleaner remains stationary. The tension in rope PQ = ?
Relevant Equations: Newton‘s Laws

The answer is 441N instead of 883N, but why? can anyone help?

I would assume it is because T1 is the total tension in rope pq, and therefore even though 2T1 =883, and T1 is pulling on both sides of the pully, it is still the same tension force in the entirety of the rope ( I could be wrong about this and if someone wishes to prove me wrong please do so)

 

[erobz]

I would assume it is because T1 is the total tension in rope pq, and therefore even though 2T1 =883, and T1 is pulling on both sides of the pully, it is still the same tension force in the entirety of the rope ( I could be wrong about this and if someone wishes to prove me wrong please do so)

Yes, that is the argument used by myself in post #5, and by @kuruman in post #6.

 

[kuruman]

$\dots~$ it is still the same tension force in the entirety of the rope $~\dots$

Yes, that's the idea. Ideal massless pulleys change the direction of the tension but not its magnitude. Pulleys with mass, as you will probably see later, change both the direction and magnitude of the tension.

 

[haruspex]

Pulleys with mass, as you will probably see later, change both the direction and magnitude of the tension.

… but only if undergoing rotational acceleration.

 

[kuruman]

… but only if undergoing rotational acceleration.

Not necessarily "only if". When the bearings of a pulley (massive or ideal) seize, you essentially have a capstan as long as there is friction between rope and pulley. The pulley does not have rotational acceleration yet the tensions on each side do not match.

 

[haruspex]

Not necessarily "only if". When the bearings of a pulley (massive or ideal) seize, you essentially have a capstan as long as there is friction between rope and pulley. The pulley does not have rotational acceleration yet the tensions on each side do not match.

My remark was in the context of "pulleys with mass [imply]". Having mass only implies a tension difference if there is rotational acceleration. Axial friction is a separate cause.

 

[gmax137]

View attachment 337562

Can I just say how much I love this image. Thanks for sharing it!

 

[PhDeezNutz]

Yeah some posters have been killing it with images. Not just @erobz but @kuruman as well (in other threads).

 

[erobz]

Yeah some posters have been killing it with images. Not just @erobz but @kuruman as well (in other threads).

Thanks for the shout out! I figure the amount of time it can take just to get on the same page, it’s just worthwhile to go ahead and make the diagram for everyone to use. Ideally the OP would do it, but it rarely seems to happen that way.

 

[kuruman]

(in other threads).

This thread too. See post #6. I am a firm believer that one figure is worth 1 kiloword.