Accelerations of connected blocks with pulleys and constraints

[Hafid Iqbal]

http://img849.imageshack.us/img849/9697/physicsy.jpg


The system bodies shown in the figure is released from rest. Assuming all the contacts to be smooth, find the acceleration of each block (mA = 14 kg, mB = 11 kg, mC = 50 kg)



This problem from Problems In Physics by Abhay K. Singh
I really confused about the answer, it said the acceleration in y-axis for B is $$a_{By}=-3a_{Ay}$$ which acceleration of each block is $$a_A = \sqrt{2}, \ a_B = \sqrt{10}, \ a_C = 1$$

I have tried to figure it out and still find $$a_{By}=-2a_{Ay}$$ and all of my answer didn't match with the answer by the author

I have had :
$$a_{Ay}=\frac{(2m_B-m_a)g}{4m_B+m_a}$$,

$$a_{By}=\frac{(4m_B-2m_a)g}{4m_B+m_a}$$,

$$a_{C} = \frac{3m_A.m_B.g}{(4m_B+m_A)(m_C+m_B)}$$

One more thing, is it true that normal force for $$A$$ is zero?

 

[tiny-tim]

Welcome to PF!

Hi Hafid! Welcome to PF!

(try using the X₂ icon just above the Reply box )

Your a_By = -2a_Ay would be correct if block C were not moving.

You'll need to add a_Cx to your a_By and a_Ay equation.

Try again (and if you still can't get it, please show your actual calculations ).​

One more thing, is it true that normal force for $$A$$ is zero?

hmm … if the diagram is correct, then A is accelerating to the right, so the normal force would have to be negative! Unless A is constrained to move in a slot, A must be hanging at an angle.

 

[Hafid Iqbal]

Hi Hafid! Welcome to PF!

(try using the X₂ icon just above the Reply box )

Your a_By = -2a_Ay would be correct if block C were not moving.

You'll need to add a_Cx to your a_By and a_Ay equation.

Try again (and if you still can't get it, please show your actual calculations ).​

hmm … if the diagram is correct, then A is accelerating to the right, so the normal force would have to be negative! Unless A is constrained to move in a slot, A must be hanging at an angle.

Hi tiny-tim, thanks for your reply! But I'm still stuck :(
Here's my complete paper work

http://img850.imageshack.us/img850/7237/unledpv.jpg ​

Phewww... And you know what, it is still wrong

 

[Iclaudius]

Wow so neat! Handwriting that is. And the colours!

 

[tiny-tim]

oooh, I like the colours!

But you're still using a_By = 2a_Ay.

You need to mark your diagram with something to show how far across C the middle pulley is.

 

[Hafid Iqbal]

Wow so neat! Handwriting that is. And the colours!

Hehe... Thanks Iclaudius... :)

oooh, I like the colours!

But you're still using a_By = 2a_Ay.

You need to mark your diagram with something to show how far across C the middle pulley is.

Hmmm... So, what is the right equation for the acceleration?
And, is my equation for mass C true?

 

[tiny-tim]

Hmmm... So, what is the right equation for the acceleration?

dunno, I haven't worked it out, I was going to let you do it, and then criticise.

(i'm good at that )

And, is my equation for mass C true?

Doing mass C on its own is not a good idea, since you need to know the reaction forces from A and B.

Do the (horizontal) equation for masses A B and C together.

 

[Hafid Iqbal]

I have tried it all over, and still can't solve it, please if anyone here know the right equation for acceleration and net force on mass C help me...

 

[tiny-tim]

The way to find the equation relating the accelerations is to find the equation relating the positions first, and then differentiate.

So call the distance from the middle pulley to the wall p, and the distance from the middle pulley to the right-hand pulley q …

then what are the x component of C, and the y components of A and B (in terms of p and q)?

 

[ashishsinghal]

Weird problem and answer but some crazy fun diagram. Never seen someone solve physics question so colorfully.
For the problems regarding acceleration use this hint: The length of string is constant irrespective of the motion.