What is the speed of a pendulum at point D?

[Quark Itself]

Homework Statement

A pendulum, consisting of a metal sphere and a massless string of length L, is initially held horizontal from a fixed support at point P. The pendulum is released from rest and it swings. It then hits a peg at point O and the distance between P and O is assumed to be Y. From there the sphere swings upwards in an arc, so what is the sphere's speed at point D?

Homework Equations

W = fdcos(theta)
KEi + PEi = KEf + PEf (i = initial and f = final)

The Attempt at a Solution

I figured that the PE is zero from point A since it's at rest and then I got stuck as the second part of the problem rose, when the sphere swings upwards.

I had a link to a picture, but it refuses to upload, but I'll try to upload it for later.

 

[Quark Itself]

http://i56.tinypic.com/2mmbq4z.png
and here's the picture that is provided for the problem

and I figured that you should split it up into components in y and x-axis directions, but still clueless from there, any tips?

 

[berkeman]

Homework Statement

A pendulum, consisting of a metal sphere and a massless string of length L, is initially held horizontal from a fixed support at point P. The pendulum is released from rest and it swings. It then hits a peg at point O and the distance between P and O is assumed to be Y. From there the sphere swings upwards in an arc, so what is the sphere's speed at point D?

Homework Equations

W = fdcos(theta)
KEi + PEi = KEf + PEf (i = initial and f = final)

The Attempt at a Solution

I figured that the PE is zero from point A since it's at rest and then I got stuck as the second part of the problem rose, when the sphere swings upwards.

I had a link to a picture, but it refuses to upload, but I'll try to upload it for later.

I believe the energy approach is the best way to go. But I would call the PE zero at the bottom, so at first, the ball has some PE due to it's initial height, and no KE, because it's at rest as you say.

Use the PEi to calculate the KE at the bottom, which gives you the initial velocity for the upward swing about the new pivot point. At the top of the second part of the swing, there will be a non-zero PE, and a corresponding KE...

 

[Quark Itself]

I believe the energy approach is the best way to go. But I would call the PE zero at the bottom, so at first, the ball has some PE due to it's initial height, and no KE, because it's at rest as you say.

Use the PEi to calculate the KE at the bottom, which gives you the initial velocity for the upward swing about the new pivot point. At the top of the second part of the swing, there will be a non-zero PE, and a corresponding KE...

Aha ! I think I get it, however, what is meant with pivot point?
so it will be like 2 simultaneous equations?
KEf of the first part of the swing will be KEi of the second part of the swing, if you understand what I mean?

 

[berkeman]

Aha ! I think I get it, however, what is meant with pivot point?
so it will be like 2 simultaneous equations?

Not sure you need simultaneous equations...

KEf of the first part of the swing will be KEi of the second part of the swing, if you understand what I mean?

Yes.

 

[Quark Itself]

Thanks for the help, but I might need to justify why PE at the bottom is of 0 value.
Why is that?

 

[berkeman]

Thanks for the help, but I might need to justify why PE at the bottom is of 0 value.
Why is that?

Gravitational PE is totally relative -- relative to some datum where the PE = 0. Where you choose that datum is up to you. I like to choose the zero PE datum at the lowest point of travel of the object, with the mindset that it takes energy to lift the object up from that datum to wherever it starts its motion from. Feel free to define your datum wherever you want -- but if you define your datum as the starting point in this problem, you will get some negative PE values. No big deal, just a little less intuitive for me personally. You will still get the correct final answer either way.

 

[Quark Itself]

Gravitational PE is totally relative -- relative to some datum where the PE = 0. Where you choose that datum is up to you. I like to choose the zero PE datum at the lowest point of travel of the object, with the mindset that it takes energy to lift the object up from that datum to wherever it starts its motion from. Feel free to define your datum wherever you want -- but if you define your datum as the starting point in this problem, you will get some negative PE values. No big deal, just a little less intuitive for me personally. You will still get the correct final answer either way.

What if the peg wasn't there? Would the PE be completely converted to KE as well, because keeping in mind that there has to be PE to lift the object upwards and thus when it goes 180 degrees swing, there has to be some PE in there converting to KE , am I right?

 

[berkeman]

What if the peg wasn't there? Would the PE be completely converted to KE as well, because keeping in mind that there has to be PE to lift the object upwards and thus when it goes 180 degrees swing, there has to be some PE in there converting to KE , am I right?

If the peg weren't there, and if the angle of the swing were not so big that the string started to buckle near the top of the swings, then the energy would be all PE at the top of the swings, and all KE at the bottom (assuming you've defined your PE=0 datum at the bottom of the swing).

 

[Quark Itself]

Ok, I think I have a grip about this problem.
Thanks a lot for your support !

 

[Quark Itself]

I have yet another problem, I seem to get a different answer from the majority of my class, can anyone go through it to check?

 

[berkeman]

I have yet another problem, I seem to get a different answer from the majority of my class, can anyone go through it to check?

Just post it in a new thread. We try to keep each thread focused just on one problem.

 

[Quark Itself]

Just post it in a new thread. We try to keep each thread focused just on one problem.

But isn't this just the same problem , being questioned? And partially unsolved?

 

[berkeman]

But isn't this just the same problem , being questioned? And partially unsolved?

Oh, I thought you were saying you had a different question. So yes, if it's still related to this problem, then it's appropriate to ask here in this thread.

 

[Quark Itself]

Well, yeah :)
The thing is now , people have gotten an answer that the speed at point D is sqrt of 4g(y-L) or it might be sqrt of 4g(L-y)
However, I get it to be sqrt of 2gy

 

[berkeman]

Well, yeah :)
The thing is now , people have gotten an answer that the speed at point D is sqrt of 4g(y-L) or it might be sqrt of 4g(L-y)
However, I get it to be sqrt of 2gy

Please show all of your work -- that makes it much easier to comment...

 

[Quark Itself]

Wnc ( Work done by non-conservative forces) = 0
Therefore : PEi + KEi = PEf + KEf
point A through point B
PEa + KEa = PEb + KEb
KEa = 0 because it’s at rest and PEb is also 0 because it reaches the lowest point of travel
thus, PEa = KEb
h = L because it is attached by the string with length L
mgl = ½mVb2
Vb = sqrt of 2gl
From point B to D
KEb + PEb = PEd + KEd
PEb = 0 Ped = mg(L-y) (because it hits the point O)
½mVb2 = mg(L-y) + ½mVd2
*m cancel out*
½Vb2 = g(L-y) + ½Vd2
Vb2 = 2gl – 2gy + Vd2
Vb2 is also equal to 2gl from previous equation so
2gy = Vd2
and thus Vd = sqrt of 2gy

 

[berkeman]

Wnc ( Work done by non-conservative forces) = 0
Therefore : PEi + KEi = PEf + KEf
point A through point B
PEa + KEa = PEb + KEb
KEa = 0 because it’s at rest and PEb is also 0 because it reaches the lowest point of travel
thus, PEa = KEb
h = L because it is attached by the string with length L
mgl = ½mVb2
Vb = sqrt of 2gl
From point B to D
KEb + PEb = PEd + KEd
PEb = 0 Ped = mg(L-y) (because it hits the point O)
½mVb2 = mg(L-y) + ½mVd2
*m cancel out*
½Vb2 = g(L-y) + ½Vd2
Vb2 = 2gl – 2gy + Vd2
Vb2 is also equal to 2gl from previous equation so
2gy = Vd2
and thus Vd = sqrt of 2gy

The only thing I see is that the height at D is 2*y, not L-y. Am I reading the figure correctly?

 

[Quark Itself]

The only thing I see is that the height at D is 2*y, not L-y. Am I reading the figure correctly?

Why would it be 2y? I don't think you've read it incorrectly.

 

[berkeman]

Why would it be 2y? I don't think you've read it incorrectly.

The radius of the smaller 2nd circle is y, isn't it? So the height the mass rises to is 2y, the diameter of the circle to get to point D?

 

[Quark Itself]

The radius of the smaller 2nd circle is y, isn't it? So the height the mass rises to is 2y, the diameter of the circle to get to point D?

Oh right, it worked.
Thanks ! :D