Calculating Pendulum Drop Distance for 45 Degree Angle - Homework Help

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Homework Help Overview

The discussion revolves around calculating the drop distance of a pendulum bob when released from a 45-degree angle, given a pendulum length of 0.44 meters. The original poster expresses confusion in deriving a different outcome compared to a previous calculation made for a 90-degree drop.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the pendulum's length and the drop distance, questioning the variables involved and the geometry of the problem. There is an attempt to derive equations based on the pendulum's setup and to clarify the definitions of the variables used.

Discussion Status

Some participants are offering guidance on visualizing the problem through diagrams and geometry rather than relying solely on energy equations. There is an ongoing exploration of the definitions of variables and the relationships between them, with some confusion remaining about the expected outcomes based on experimental data.

Contextual Notes

Participants note discrepancies between calculated drop distances and experimental values, particularly questioning the validity of the experimental results at different angles. There is a request for clarification on the experimental setup and variable definitions to better understand the problem.

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Homework Statement


i need to calculate the d for a 45 degree drop of pendulum that the length is .44m. i did the one for 90 degrees but i can't figure out how to get a different outcome.


Homework Equations


ug initial= KE + Ug final
mgh=0.5mv^2=mgh
gl=0.5rg+g2r
l=0.5r+2r
l=0.5(l-d)+2(l-d)
l=5/2l-5/2d
l=d+r
r=l-d
v^2=rg
m(v^2/r)=mg


The Attempt at a Solution


i got 26.4 cm
L=.44m
dexp=.28 @90 degrees
dexp=.41 @ 45 degrees
 
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I would like to lend a hand but I am a little confused about the variables you are using.

If I interpret correctly,
L=length of pendulum string (0.44m)
d=height of pendulum bob at θ=45° (unknown)
r=difference between L and d (unknown)

If this is the case you don't need to worry about energy or forces. Drawing a diagram and looking at the geometry of them problem will be enough to find and equation for d in terms of what you already know.
A good place to start would be to notice that L and r form a right triangle when the bob is held at 45°.
 
ok so i drew this and i get that the r is what's left of the length of the string after it hits d. r is also the radius of the circle that the bob makes when it makes one revolution. i don't understand how to get either one of them.

L=1/2r+2r
L=3/2r
0.44=3/2r
r=0.2933333
i guess this is how i could find that and if i plug this in...

r=L-D
-D=r-L
D=-r+L
D=L-r
D=0.44-0.29333333
D=.129067m
D=12.9cm
that doesn't make sense because the Dexp= .41
thats .28m off...
the Dexp@90 was only 1.6cm off...
please help
 
Sorry, but I'm still a little confused here...

I see your experimental d, called dexp, at 45° is larger than your dexp at 90°.
With the way I've defined d above, this should not be possible, so perhaps I do not understand the experiment correctly.

Could you start at the beginning and describe the experiment? (and possibly include a picture?) Defining any variables you use would also be very helpful.
 
Last edited:

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