Rank Kinetic Energy Pendulum Problem: A-E-I < B-F < D-H < C-G

[sona1177]

Homework Statement

I have a pendulum problem that shows me the picture of the pendulum, which Physics Forums won't let me copy and paste. but anyway it is the picture of a pendulum that starts at point A, goes down to point B, then C (lowest point), then up to D (which looks the same height as B), and then up to E (which looks the same height as A). Then the pendulum comes back down to point (F), then down to G, which is again the lowest point, then back up to H, and finally I, which is the last point I see. If that image is clear, can someone help me rank the kinetic energies from smallest to largest?

Basically the pendulum swings back and forth, (once forward, and then back).

My answer was A,E, I < B,F < D,H < C,G but that is wrong. Can someone please help me?

Homework Equations

The Attempt at a Solution

 

[Stonebridge]

Without the diagram it's rather difficult.
You say D "looks the same height" as B.
If it is the same height then the kinetic energy at D will be the same as at B.
In which case the ranking is wrong because you have B<D [and F<H]

 

[sona1177]

Without the diagram it's rather difficult.
You say D "looks the same height" as B.
If it is the same height then the kinetic energy at D will be the same as at B.
In which case the ranking is wrong because you have B<D [and F<H]

Ok so would B, F, D, and H all be equal then?

So the order would be A, E, I <B, F, D, and H< C, G

Doesn't time make a difference? Wouldn't the pendulum swing slower when it's swinging for the second time (E ->I)?

 

[Stonebridge]

If at the same vertical height, then B,F,D and H will all be the same.
Yes, so will A,E and I.

Questions like this usually say something like "ignore friction".
If this is the case the pendulum will actually swing for ever. The ke at any point will be such that the sum of ke plus pe will be constant.
In this case, as the pe depends only on the vertical height of the mass (=mgh) then the ke also only depends on the vertical height. ke=total - pe

If the pendulum is slowing down, due to friction, then yes, it depends on time.
There is nothing in the question as I read it to suggest which is the case. I have assumed no friction.
Maybe if I could see the diagram I could be more helpful.
If the final point is at the same height as the initial, A and I, then in one swing there has been no loss in energy. So the frictionless case would be the correct one.

 

[rwisz]

I can provide a response to this content. It seems like the problem is asking for the ranking of the kinetic energies at different points of the pendulum's motion. To accurately rank the kinetic energies, we need to consider the factors that affect kinetic energy, which are mass and velocity.

At point A and E, the pendulum has the same height and therefore the same potential energy. However, at point A, the pendulum has the highest velocity as it is at the bottom of its swing, so it also has the highest kinetic energy. At point E, the pendulum is at the same height as A but it has a lower velocity as it is at the top of its swing, so it has a lower kinetic energy.

Similarly, at point B and F, the pendulum has the same height but at point B it has a higher velocity and therefore higher kinetic energy. At point F, it has a lower velocity and therefore lower kinetic energy.

At point C and G, the pendulum reaches its lowest point and has the highest potential energy. However, at point C, it has zero velocity and therefore zero kinetic energy. At point G, it has a non-zero velocity and therefore has a non-zero kinetic energy.

At point D and H, the pendulum is at the same height and has the same velocity, so it has the same kinetic energy at both points.

Based on this analysis, the correct ranking of the kinetic energies would be: A,E > B,F > D,H > C,G. This is because at point A and E, the pendulum has the highest velocity and therefore the highest kinetic energy. At point B and F, it has a lower velocity and therefore lower kinetic energy. At point C, it has zero velocity and zero kinetic energy, and at point G it has a non-zero velocity and non-zero kinetic energy. At points D and H, the pendulum has the same velocity and therefore the same kinetic energy.

I hope this helps to clear up any confusion and provides a correct ranking of the kinetic energies in this pendulum problem.