whats the difference? (dynamics)

[Moody Boy]

this question is belong to 4th edition of J.L . Meriam >>> prob 3/23

i wanna know whats the difference between these two cases?

why the accelerations come difference ?

 

[cypress]

There is a difference in net force acting on the 30Kg mass. In case a the tension on the rope is given. In case b it is not given and the tension is not the same. Do you see why?

[Moody Boy]

There is a difference in net force acting on the 30Kg mass. In case a the tension on the rope is given. In case b it is not given and the tension is not the same. Do you see why?

 

why its not the same?? here's my prob

i think in case "b" is given too, tha mass is 20 kg so the tension on that side is (20g) just like case "a"

thanks for helpin me out

Edited December 5, 2010 by Moody Boy

[cypress]

why its not the same?? here's my prob

i think in case "b" is given too, tha mass is 20 kg so the tension on that side is (20g) just like case "a"

thanks for helpin me out

 

Try this thought exercise to help you see why it is not the same:

 

Imagine that the 20 kg block is hung on a rope fastened securely to the celling. I am fairly certain you will agree the force/tension on the rope is 20*9.81 N right?

 

But cut the rope so the block is accelerating downward at 9.81 m/s² Now what is the tension on the rope?

 

Now consider the rope is wrapped around a winch that is capable of maintaining fixed tension so that the block is accelerating downward at 4.905 m/s². What is the tension on the rope (being maintained by the winch)?

Edited December 5, 2010 by cypress

[Mr Skeptic]

Well there's two separate issues here:

1) 20 kg is not 20 N (although I guess what they're showing is 20 kg * 9.81 m/s^2, so see #2).

2) If the appropriate mass were added such that it would weigh 20 N, then the tension on the rope would be less than 20 N due to the acceleration (compare to, if a dog tugs on the leash and you follow the tension on the leash is not as much as if you stay still).

3) And then you have to consider that adding that new mass changes the mass of the system.

 

But I'd have to calculate to be able to say which of these has the greatest effect.