Calculating Pendulum Drop Distance for 45 Degree Angle - Homework Help

[mitchmcsscm94]

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

 

[chrisd]

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°.

 

[mitchmcsscm94]

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

 

[chrisd]

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.