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.

 

[asteriatic]

Great job on attempting to solve this problem! To calculate the drop distance for a 45 degree angle, you can use the equation L = d + r, where L is the length of the pendulum, d is the drop distance, and r is the radius of the pendulum. Since the length of the pendulum is given as 0.44m, we can substitute this value into the equation as follows:

0.44m = d + r

Next, we can use the equation v^2 = rg to solve for the radius, r. This equation relates the velocity (v) of the pendulum to the radius (r) and the acceleration due to gravity (g). Since we know the velocity at the bottom of the pendulum is 0 (since it stops momentarily before swinging back up), we can set v = 0 and solve for r:

v^2 = rg
0 = rg
r = 0

Now, we can substitute this value for r into the equation L = d + r and solve for d:

0.44m = d + 0
d = 0.44m

Therefore, the drop distance for a 45 degree angle is equal to the length of the pendulum, which is 0.44m. This is different from the drop distance for a 90 degree angle, which you correctly calculated as 0.28m. This makes sense because the angle affects the length of the pendulum, and at a 45 degree angle, the pendulum is shorter than at a 90 degree angle.

Keep up the good work in your studies!