Question about a crane and anchor

[homeylova223]

Homework Statement

Tension on crane.

Relevant Equations

No equations are used.

The question is number 25. Where is the tension on X greater. I think it would be A because you have the weight of not only box A but also the anchor pulling down on the rope.

 

[Merlin3189]

Yes it is A, but your reason is wrong.
It asks if the tension in X is more when the weight is at A or at B. X carries the weight of the anchor in both cases, so is irrelevant.
At A, the weight increases X tension. At B, the weight decreases X tension,

 

[jbriggs444]

Yes it is A, but your reason is wrong.
It asks if the tension in X is more when the weight is at A or at B. X carries the weight of the anchor in both cases, so is irrelevant.
At A, the weight increases X tension. At B, the weight decreases X tension,

I disagree with this, however the drawing is a marvel of ambiguity, making it difficult to guess the intent.

As I interpret it, the joint in the middle where horizontal beam meets vertical column is to be interpreted as a hinged joint where both the leftward-extending and rightward-extending portions of the horizontal beam are free to swing independently up and down. The vertical column is also to be viewed as being hinged. The upward-extending and downward-extending portions are free to pivot independently.

The rope is anchored to the top of the column. It is not free to move left or right relative to the column. However, as above, the column itself is free to pivot, constrained by the rope.

The left end of the left-extending beam is anchored to the "anchor". It is not free to move in any direction. The left end of the rope is anchored to the left-extending beam. Accordingly, it is not free to move in any direction.

The bottom end of the downward-extending column is anchored to the floor. It is not free to move in any direction.

The right end of the rope is anchored to the right end of the right-extending beam.

With these constraints and freedoms we can see that the column elements are subject to compressive loads only. The beam elements are also subject to compressive (or tensile) loads, but support the load (at point A or point B) based on stiffness.

Do a torque balance for the rightward-extending beam with the weight at position B and see what that implies for the tension in the rightward extending rope section.

Here is a drawing showing my interpretation:

 

[homeylova223]

In weight B the string is longer would that increase tension I wonder.

 

[jbriggs444]

In weight B the string is longer would that increase tension I wonder.

No. That is not [completely] correct reasoning. Some trigonometry is called for.

 

[Merlin3189]

I disagree with this, however the drawing is a marvel of ambiguity, making it difficult to guess the intent.

Yes you're right.

I was just working on an update, but will leave it unposted, as you've left it for OP's consideration.

What mislead me was the "crane". As U say it's just a board fixed at one end.

Considering the points you made about the possible arrangements of string and support, I decided whatever they are does not affect the outcome. But I'll wait and se how this develops.

I must agree the question (like several others on the paper) is unclear and ambiguous.

Also I disagree with some answers. In the flight section, they still seem to believe in the equal transit time for aerofoils, which I thought had been discredited.