Rotational Mechanics Problem: Solving for Height Using Energy Conservation

[thunderhadron]

Hi Friends I am getting some problem in solving this question every time with the help of energy conservation. Please help me out. Here is the question

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn1/s480x480/32407_2637149505288_842292859_n.jpg

Well I am doing that thing ,

By energy conservation,

Total energy initially = Total energy final

i.e. Kinetic Energy of block + ring = Potential energy of Bock + ring

i.e.

1/2 mv² + 1/2 mv² + 1/2 Iw² = mgh

mv² + 1/2 mr²(ring). v²/r² = mgh

afer solving this h = 2v²/g


But answer is always option (b).

Please friends help me out in this problem. I will be very thankful to all of u guys.

 

[Tanya Sharma]

Hello thunderhadron...

The block B has no initial velocity,hence,no intial kinetic energy.Initially ,only the ring has translational and rotational kinetic energy.When the ring attains maximum height , what will be the motion of the block B ??

 

[Basic_Physics]

The problem states that initially the block is stationary.

 

[thunderhadron]

Hello thunderhadron...

The block B has no initial velocity,hence,no intial kinetic energy.Initially ,only the ring has translational and rotational kinetic energy.When the ring attains maximum height , what will be the motion of the block B ??

Hi Tanya, Thank you for the reply.
The Block will be doing linear motion and ring will also be doing linear along with it as seen from the ground.

But the major issue is that which law I should use to deduct block's velocity with respect to ring, when the ring is at the max height..

 

[ehild]

The block and ring make a system, and is no horizontal external force. What is conserved in addition to energy?

ehild

 

[Saitama]

I am trying to solve this problem but it seems that I am missing out something while conserving energy. Initially, the ring has kinetic energy (rotational+translational). When the ring is at maximum height, the ring and the body B, both have kinetic energy too. But when I solve it, I don't get the right answer.

 

[Tanya Sharma]

The Block will be doing linear motion and ring will also be doing linear along with it as seen from the ground.

Initially the block is stationary,hence it will have no kinetic energy.

But the major issue is that which law I should use to deduct block's velocity with respect to ring, when the ring is at the max height..

When the ring is at the maximum height,it will be at rest with respect to the block.Isnt it?? If this wasnt the case , how else can we deduce that the ring has attained maximum height .

Now ,regarding what is the common velocity of the ring and the block when the ring attains max height,what do you think are the forces acting on the system(ring+block) ? What can be conserved ?

 

[ehild]

I am trying to solve this problem but it seems that I am missing out something while conserving energy. Initially, the ring has kinetic energy (rotational+translational). When the ring is at maximum height, the ring and the body B, both have kinetic energy too. But when I solve it, I don't get the right answer.

The text is not clear. It says that the ring rolls on the horizontal part of the body B, and the surfaces are smooth. That means no friction between the ring and B, so the ring can not roll on the surface of B. I think the problem should be interpreted that the ring was rolling before reaching B and it keeps the initial rotation energy during its motion.

ehild

 

[Saitama]

...it keeps the initial rotation energy during its motion.

How?

If I do as you say, i get the option b) but why it keeps its intial rotational energy?

 

[ehild]

What changes it if there is no friction? Think of a tyre on ice.

If the ring keeps rolling along the surface of B, it becomes in rest with respect to B at the end and looses all rotational energy. At what height?

ehild

 

[thunderhadron]

Initially the block is stationary,hence it will have no kinetic energy.



When the ring is at the maximum height,it will be at rest with respect to the block.Isnt it?? If this wasnt the case , how else can we deduce that the ring has attained maximum height .

Now ,regarding what is the common velocity of the ring and the block when the ring attains max height,what do you think are the forces acting on the system(ring+block) ? What can be conserved ?

I was not saying for the starting time at t = 0. My total statements were for (after t = 0).
and I know that linear momentum is also conserved along with that but still I m not getting the answer.

mv = 2mv'
i.e. v' = v/2

1/2 mv² + 1/2(mr²)v²/r² = mgh + 1/2. (2m) (v/2)²

after solving this,
h = 3v²/4g

which is not correct. Isn't it.

So please try to get correct approach. There is something missing here still.

 

[ehild]

You assumed that the rotational energy becomes zero at the end. The book assumes that it is unchanged.

ehild

 

[thunderhadron]

You assumed that the rotational energy becomes zero at the end. The book assumes that it is unchanged.

ehild

Thank you I got the correct answer and explanation.
thank you ehild.