Your boss at the Cut-Rate Cuckoo Clock Company asks you whatwould happen to the frequency of the angular SHM of the balancewheel if it had the same density and the same coil spring (thus thesame torsion constant), but all the balance wheel dimensions weremade one-third as great to save material.

a)By what factor would the frequency change?

b)Would the frequency increase or decrease by the factor foundin part (a)?

c)By what factor would the torsion constant need to be changedto make the smaller balance wheel oscillate at the originalfrequency?

d)Would the torsion constant need to be increased or decreasedby the factor found in part (c)?

Answer:

a) the factor between the frequencies is      f ’/ f₀ = 9

b) the frequency increases        f ’= 9 f₀

c) So that the frequency is equal to the initial one      k ’= k₀ / 81

d) the torque constant must decrease

Explanation:

This is a simple harmonic motion, like angular velocity

       w = [tex]\sqrt{\frac{k}{I} }[/tex]

where k is the torsion constant and I the moment of inertia of the flywheel.

Angular velocity and frequency are related

       w = 2π f

we substitute

       [tex]f= \frac{1}{2\pi } \sqrt{\frac{k}{I} }[/tex]        (1)

We will use the subscript o for the system without change

      f = [tex]\frac{1}{2\pi }[/tex]  [tex]\sqrt{\frac{k}{I_{o} } }[/tex]

In the problem they indicate that the torsion constant remains constant, therefore we must analyze the moment of inertia, in general the flywheels are circular discs,

       I = ½ M R²

Let's find the change when reducing the radius r ’= r / 3

Let's use the density

       ρ = m ’/ V’

       m ’= ρ V’

disk volume is

       V = π r² e

suppose that the thickness is small and does not change, substitute

      m ’= ρ π[tex](\frac{r}{3}) ^{2}[/tex] e = 1/9 m

Moment of inertia

     I ’= ½ m’ r’²

     I ’=[tex]\frac{1}{2}[/tex] [tex]\frac{1}{9}[/tex] m (\frac{r}{3}) ^{2} = 1/81 (½ m r²)

     I ’= 1/81 Io

we substitute in equation 1

    f ’= [tex]\frac{1}{2\pi }[/tex] \sqrt{\frac{k}{I} }

    f ’= \frac{1}{2\pi }   \sqrt{\frac{81k}{Io} }

    f ’= 9 f₀

Let's analyze the questions

a) the factor between the frequencies is

        f ’/ f₀ = 9

b) the frequency increases

        f ’= 9 f₀

c) So that the frequency is equal to the initial one

      k ’= k₀ / 81

d) the torque constant must decrease

Which of these provides the best evidence for Newton’s First Law of Motion?

A
While sitting in a chair, you exert force on the chair, and the chair exerts the same amount of force back on you.

B
A basketball sitting on the basketball court doesn’t move until something pushes it.

C
You push a full shopping cart and an empty shopping cart. The empty shopping cart goes much faster than the full one.

D
You push your little brother on the swings, and he goes higher the harder you push him.

Hello, can anyone help me with this question?

Does anyone know this or done it? It’s for life skills and about MyPlate:)

Please match word and definition

Question 10 options:

flow of an electrical charge in a circuit


Prevents electrons from moving


provides a path for electrons to flow


electrons and electric current move easily

1.
electric current

2.
insulator

3.
electric circuit

4.
conductor

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The distance between two crests of a wave is called 'wavelength*
true
false

HELPPPPPPP!!!!!!!!!!!!!!!!

Explain how the perfume atomizer works under Bernoulli's principle

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A. 400 m
B. 160 m
C. 2.5 m
D. 20.4 m

The kinetic theory and the caloric theory are the same. true or false

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A. Gravitational
B. Weak nuclear
C. Strong nuclear
D. Electromagnetic
SUBMIT

2. Which of the following changes on different celestial objects due to the
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A. mass
B. weight
C. height
D. width

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You are riding a bicycle. You apply a forward force of 100 N, and you and the
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bicycle?
A. 1.5 m/s2
B. 1.8 m/s2
C. 1.25 m/s2
O D. 0.8 m/s2
SURN

2
1 point
Which of the following is an example of an allele?
axial flowers
all of the above
1
a
2
ОО
AA
3
Previous

23. What is the total resistance of the combination of two resistors in the diagram?
A. 0.03
B. 0.15
C. 6.67
D. 30​

Plate techtonics refers to the theory that

A body at rest will remain at rest unless acted on by a(an) _____.

Question 1 options:

A. external, unbalanced force.


B. external, balanced force.

A black hole's gravitational field is unchanged
True
False

Bob Beamon's 1968 Olympic long jump set a world record which remains unbroken to this day. This amazing jump resulted from an initial velocity of 9.5 m/s at an angle of 40 degrees from the horizontal.
1. Calculate the initial horizontal velocity (V_ix) to two significant figures:

2. Calculate the initial vertical velocity (V_iy) to two significant figures:

3. Calculate the time needed to reach the highest point of the jump (t_1/2) to two significant figures:

4. Calculate the total time (t_TOT) needed to complete the jump to two significant figures:

5. Calculate the maximum height (h) reached during the jump to two significant figures:

6. Calculate the range (total horizontal distance) of his jump to two significant figures:

Which system is used for transporting molecules to the cells?

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The quantity of matter in an object. More specifically, it is the measure of the inertia that an object exhibits in response to any effort made to start it, stop it, or change in any way its state of motion

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A. The rock cycle only affects objects that are too small to be observed directly.


B. The rock cycle is only an abstract idea and does not actually occur in nature.


C. The rock cycle no longer occurs on Earth.


D. The rock cycle takes too long to be able to observe it in entirety.

Can I have some help please :)

Based on the displacement graph below, which divider is likely to experience the greatest negative acceleration?

A. The divider originally located at 1 unit.
B. The divider originally located at 4 units.
C. The divider originally located at 7 units.
D. The divider originally located at 10 units.

Explain how water waves are not purely transverse waves