How Does Tension Vary Along a Rope in Motion?

[lmlgrey]

1. 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.

1. The velocities of points A and B are equal. TF
2. Greater than Less than Equal to The acceleration of the point O is ... the acceleration of the block. TF
3. Greater than Less than Equal to The tension at the point B is ... the tension at the point A. TF


click to see the diagram: http://b.imagehost.org/0991/rope.gif




2. Is the tension equal everywhere on a heavy rope?

 

[Doc Al]

Show what you've figured out so far.

 

[lmlgrey]

3. the tension at point b is EQUAL TO the tension at point a
because tension force is equal everywhere on a string/rope

2. The acceleration of the point O is GREATER THAN the acceleration of the block
bcause based on #3, when the same net force is given, the smaller the mass, the greater the acceleration... O is obviously lighter than the box, therefore, has a greater acceleration.

3. the velocities of A and B are equal

true, since the accelerations of A and B are the same

... above is what i figured out so far, but they are wrong judged by the website.

 

[Doc Al]

3. the tension at point b is EQUAL TO the tension at point a
because tension force is equal everywhere on a string/rope

That would be true for a massless rope, but that's not what you have here.

2. The acceleration of the point O is GREATER THAN the acceleration of the block
bcause based on #3, when the same net force is given, the smaller the mass, the greater the acceleration... O is obviously lighter than the box, therefore, has a greater acceleration.

3. the velocities of A and B are equal

true, since the accelerations of A and B are the same

Aren't all the points... O, B, A, P... connected together?

 

[lmlgrey]

I noticed that its a heavy rope... but I don't understand the difference it makes..
so the tension force is not constant throughout the rope?\

and yes, A,B,O,P are points on the rope therefore, connected.

 

[Doc Al]

I noticed that its a heavy rope... but I don't understand the difference it makes..
so the tension force is not constant throughout the rope?\

The tension at each point is the force that the rope exerts at that point. Compare the force needed at point O, which pulls on everything to the right of point O, to the force needed at point A, which pulls on everything to the right of point A. Do those forces pull on the same amount of mass? Can they be the same force?

and yes, A,B,O,P are points on the rope therefore, connected.

Right, they are all connected. So how can one point have a different acceleration than another?

 

[lmlgrey]

Okkk. I see!
I can interpret it as it is a massless rope, but there is each an object that attaches at A,B,O,P which weighs the same... ok, now I get it. The acceleration would be the same since the the whole system has only one acceleration but tension force is different since there are different masses.

thank you very much for the hints!