Physics cuckoo clock shm? - cuckoo clock parts
His boss at the cutting speed Cuckoo Clock Company asked what is the angular frequency of SHM's on bike, if I have the same density and the source itself (ie, had) the same torque, but all measurements, the third wheel is great for storing materials.
a) By what factor would change the frequency?
b) increasing the frequency or decrease the factor in paragraph (a)?
c) By what factor would have to change some constant, so that the smaller area of the unbalance to the original frequency?
d) if the torsion constant need to be increased or decreased by the factor in paragraph (c)?
Friday, January 22, 2010
Cuckoo Clock Parts Physics Cuckoo Clock Shm?
3 comments:
Part A:
As I explained in my physics class, the frequency f = omega/2pi where omega = sqrt (k / I) and in the case of simple harmonic motion, angular, where I the moment of inertia about the axis of the balance wheel, K is the torsion constant.
Take the equation f = omega/2pi. The 2ft remains the same, directly affects the omega-f - are directly proportional to the other. Thus we find the change in the omega, and change frequency.
omega = sqrt (k / I). Suppose that the torsion is constant at first, because we are trying to find the influence of an unbalanced account.
I = WRC ^ 2, with the radius of C is a constant which depends on ignoring the shape or weight, and R. Since C is constant, too.
They know that all the dimensions of 1 / 3 of the original will. In calculating the surface of a solid disk is pi r ^ 2 * H. Thus R 1 / 3, H 1 / 3.
I = MR ^ 2 = (pi r ^ 2 h) * (R ^ 2). Pi is a constant, then ignored.
I = (1 / 3) ^ 2 * (1 / 3) * (1 / 3) ^ 2. This means that I = 1 / (3 ^ 5), or I = 1 / 243
In turn, fdirectly proportional to omega = sqrt (k / I) = sqrt (k / (1 / 243)) = sqrt (243k). K ignored, because it is a constant in this case, and the answer is 15.6
Part B:
By the simple logic that if something is smaller, the frequency increases.
Part C:
Now it is constant, and the change of k. To make things balance,
omega = sqrt (K / L) for k = 1, and I must be, so that the sqrt (1) = 1.
k / I = 1
k = 1 * I = 1 / 243.
In other words, the torsion constant should be 1 / 243, or change the factor 243rd
Part D:
Since the torsion is constant, then 1 / 243, which resulted in a decline, the increase due to small size.
I'm curious because I always thought that cuckoo clicks by a typical gravity pendulum. For a torsion pendulum in the frequency can be expressed) by (ref1
(a) = f (1/2pi) sqrt (k / I)
f - Frequency
K-wire spring constant torque /
I - moment of inertia of the pendulum.
The problem is the wheel alignment, as its geometry determines I (see Ref # 2)
assume a simple case of hard
I =. 5 MR ^ 2
then
F1/F2 = (1/2pi) sqrt (k / 5 m r1 ^ 2) / (1/2pi) sqrt (k / 5 m r2 ^ 2) =
F1/F2 = sqrt (R2 ^ 2/r1 ^ 2) =
F1 = F2 = R2/R1
because he, the size of 13 r2 = 1/3R1
and F1/F2 = (1 / 3 R1) / R1 = 1 / 3 = r then
f2 = 3F1
(b) the frequency increases 3 times
(c) we must apply,
f = (1/2pi) sqrt (k / I)
and we find that can be solved by reducing the k 1 / 9 this problem alone.
(d), see (c)
Edward,) by his side is not correct. (I have the same problem as Paul).
I first thought, as he did, that a "third of the great might" only for radio, and I =. 5Mr ^ 2, then shows 1 / 3 ^ 2 = 1 / 9, and joining (1/2pi) sqrt (k / I) that are 3 of the square root would be, but he says the answer is wrong. This is logical, because you plug in 1 / 3 of R and call it a day can. This means that the total mass of the system remains the same, but the radius is reduced. But mass is reduced (at least I assume it is). So after that I =. 5 (M / 3) (R / 3) ^ 2 means that we are an extra 1 / 27 with I and a connection to our "F" from the equation, we get sqrt (27), the frequency difference. However, I have also tried to answer this, and it was not correct. I tried some other stuff, so you all the bad answers I could find so far: (1 / 9), (1/sqrt3) sqrt3, 3 and sqrt27.
I'm sure that was the fault of assumptions about what is "all aspects of weight, one third of theIdeal for storage "refers to the dynamics of the wheel. Maybe 1 / 3 radius and thickness, but the mass is a fraction? There seems to be a circumvention of the scope of this course, however.
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