Pendulums and displacement angle

[ilovemedi]

Are both angles the "displacement angle"? There's a question in TBR physics, page 253:

Question : All of the following statements are true w/ respect to the total energy of the system EXCEPT:

A) KE of the bob increases uniformly as the bob descends.
B) PE and KE energy are = to one another at a time that is 1/8th of the period after it had all gravitational potential energy.
C) Increasing the initial displacement angle will increase the maximum KE of the system.
Answer: A

I thought it was C, because when it's straight down (where the angle is zero), that the KE is the maximum. So as the angle increases (and goes towards the left or right), PE increases, while KE decreases. So increasing displacement angle decreases KE because PE goes up.

I also have no idea why B is true and why A is incorrect (I thought KE = 1/2mv^2 and increases constantly/uniformly as it goes down).

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[591489]

Ok lets go through these one by one.

1) Firstly, I don't like the way this is worded so I understand your confusion. Let me try to explain what I think they are asking. Velocity is increasing constantly (since there is acceleration from grav) and KE is proportional to the square of the velocity. So, think about what the shape of KE as a function of V would look like...it would look like y = x^2. That is not "uniform."

2) Where is the KE equal to the PE?
Answer: half way between the point where all the E is KE and all the E is PE (aka between h = 0 and h = h)
1 swing from all the way right to all the way left is half a period. So a swing from h = h to h = o is 1/4 a period. Thus, half way between h = 0 and h = h (aka the point where KE = PE) is 1/8th a period.

3) Increasing initial disp. increases initial PE (which is also the max PE). The max KE = max PE.

Hope that helps.

 

[Blueprint MCAT Tutor]

Heya - I think you're misreading the question.

Here's my explanation (scroll down):

http://forums.studentdoctor.net/threads/specific-science-questions.1053558/

Hope this helps! 🙂

-Bryan

 

[ilovemedi]

Ok lets go through these one by one.

3) Increasing initial disp. increases initial PE (which is also the max PE). The max KE = max PE.

Hope that helps.

Thanks @Knattagh and @mcatguru . I'm still a bit confused on the wording of "intial displacement angle". So just to recap: increasing INTIAL displacement angle means that the string is pulled AWAY from the middle (where KE=max or angle = o degrees) AND to the right or left, for example? And is initial PE = max PE = max KE always true for pendulums?

 

[591489]

Yes to your first question. You can think of the initial displacement as how far up the bob on the pendulum moves while the string is taught.

As for your second question, as long as there is not friction anywhere, I can't see why not. Since initial displacement defines how much energy you have because initial displacement sets you h in the energy equation E = mgh.

 

[neurodoc]

The OP's question was: Are both angles the "displacement angle"?
The two angles are equal. The upper angle in the diagram is what is
usually called the displacement angle of the pendulum, but since they
are equal, the answer to the original question is "Yes."