Why is the tension different in two systems with the same downward force?

[Cursed]

Homework Statement

I just want to know why the tension in the rope in system A is not equal to 100 lbs, while the tension in the rope in system B IS 100 lbs.

[PLAIN]http://img823.imageshack.us/img823/9462/conceptualquestion.png

In system A, a 100-lb mass is hanging. In system B, there is a 100-lb downward force.

The question asks: Find the acceleration of the 200-lb block.

Homework Equations

None.

The Attempt at a Solution

For system B,
T - mg = -ma
(100 lb) - (200 lb) = - (200 lb/ 32.2ft/s) a, a = 16.1 ft/s^2

 

[Dadface]

In system B the question tells you that the tension is 100lb whereas for system A you are not told what the tension is.Let the tension=T
For the 200 lb weight.... 200-T=200a
For the 100 lb weight.... T-100=100a

 

[ashishsinghal]

Let me tell this to you another way:
Let us assume that tension is 100lbs. Then the blue box will have no acceleration. but red box will have acceleration and hence blue block should also have acceleration. Hence contradiction.

In the other case I do not think that they have mentioned that tension is 100 lbs. Let us concentrate on the particle on which the force 100 lbs is acting. We are taking rope to be of negligible mass.Hence the particle is of negligible mass. Hence any finite force in any direction on the particle would create infinite acceleration. Hence for acceleration to be finite, negligible force should be acting on it. Due to this tension in the rope is equal to 100 lbs

 

[Mr.A.Gibson]

A and B are equivalent, the tension is the same.

 

[ashishsinghal]

A and B are equivalent, the tension is the same.

No, they are not. Read the above 2 posts for your understanding and then reply.

 

[Mr.A.Gibson]

No, they are not. Read the above 2 posts for your understanding and then reply.

I have read them thank you, the first post is fine a simultaneous equation. And from it T = 133lb, I now see that they are not equivalent as the mass being accelerated is larger in the first example

I couldn't really understand your post. Especially as the string is a means to transfer force therefore its mass is of not consideration. Perhaps I am being slightly confused by american units especially the use of a unit of mass (lb) to describe a force. You seemed to say the the tension was not 100lb but then deduce that it was??

 

[Dadface]

I'm having the same problem with the units as you Mr Gibson.(Anyone looking at the equations should take into account that the weights should be expressed in units of pound force as distinct from the masses which are in pounds.Is that right?)

My Thursday rant:

Why do some people still use these old fashioned and confusing units?Rant over.

ashishsingal I think it is implicit in the question that for B the tension is 100lb but I agree that it is not stated to be so.Perhaps the OP will report back and clarify the question.If you wish to consider a particle of negligible mass on the rope remember that there are two forces acting on it.

 

[ashishsinghal]

If you wish to consider a particle of negligible mass on the rope remember that there are two forces acting on it.

Yeah, that is what my point is. The first force is the 100lb one, the other is tension. They act in opposite direction. Since they need to make net force on the particle zero, they need to cancel out each other. due to this tension is 100lbs

 

[Dadface]

Yes I agree.Nicely analysed as a good first approximation.

 

[ashishsinghal]

Thank you.