Simple Forces Question with Diagram

[lillybeans]

Homework Statement

The following is a physics problem taken directly from my online assignment. As you can see, I only have 6 attempts available in total and I have already exhausted 5/6:

As shown in the diagram, someone is pulling on a HEAVY straight rope with force F. Points A and B are one quarter of the distance from each end, and points O and P are the ends of rope. The rope is attached to a heavy block, which slides on a frictionless floor, and which therefore accelerates as it is pulled.

Select the appropriate choice for each of the following statements: True, False, Greater than, Less than, or Equal to For choices involving comparisons Greater than, Less than or Equal to, consider only the magnitudes of the quantities being compared.

Homework Equations

F=ma

The Attempt at a Solution

To begin with, I am now definitely sure of the following:

1.___
2. Less than
3.___

For 1&3, I think 1 should be false and 3 should be true, because technically you can treat the rope and the box as one object and they are both accelerating/moving at the same rates. However, I'm not sure what the hint "think of each quarter of the rope as a separate mass" is trying to say. Is it implying that if an object is long enough, different parts of the SAME object will move/accelerate at different rates simply due to their position relative to each other? But how can the rope not SNAP if the front of the rope is moving/accelerating at a faster rate than the rear? So if not, I say 1 is false, 2 is less than, 3 is true. Any opinions and help would be greatly appreciated. Too scared to press the submit button right now; it's my last chance left.

And here are the previous attempts, all of which are incorrect (the fourth one was a stupid waste):

True
Greater than
False

False
Equal to
False

True
Equal to
False

Equal to
Equal to
False

False
Less than
False

 

[rl.bhat]

So if not, I say 1 is false, 2 is less than, 3 is true.
Try this option.

 

[lillybeans]

So if not, I say 1 is false, 2 is less than, 3 is true.
Try this option.

I finally tried it (very scared to press the button), but i did get it right this time! thanks!

 

[PeterO]

I finally tried it (very scared to press the button), but i did get it right this time! thanks!

Explanation:

a string is usually considered unstretchable so the acceleration and velocity of all parts of the string and the block will be the same throughout.
The key to part (b) is that the rope is heavy [we usually have a light/mass-less string]

Imagine the rope has a mass of 1 kg, and the Block has a mass of 1 kg.

if F was 2N, then it would cause an acceleration of only 1 m/s² to the 2kg combination.

For that acceleration, the rope is only transmitting a force of 1N through to the block.

Now reality won't be that extreme - they did say it was a heavy block - but still the force on the block will be slightly less than F.

 

[omaroao]

Guys, what if it was this The acceleration of the point A is ... the acceleration of the point P. What would be the answer, same question ?? Please reply, i have one try left.

 

[PeterO]

Guys, what if it was this The acceleration of the point A is ... the acceleration of the point P. What would be the answer, same question ?? Please reply, i have one try left.

I paste part of my previous post:

Explanation:

a string is usually considered unstretchable so the acceleration and velocity of all parts of the string and the block will be the same throughout.