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frosja888 [35]
3 years ago
10

A holiday ornament in the shape of a hollow sphere with mass 0.010 kg and radius 0.055 m is hung from a tree limb by a small loo

p of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum with negligible friction. Calculate its period. (Use the parallel-axis theorem to find the moment of inertia of the sphere about the pivot at the tree limb.)
Physics
1 answer:
poizon [28]3 years ago
3 0

Answer:

0.608 s

Explanation:

Given that

m = 0.01 kg

r = 0.055 m

the period of a pendulum is primarily stated as

T = 2π √(I/mgd), where

I = moment of inertia

m = mass of pendulum

g = acceleration due to gravity

d = radius

moment of inertia, I is given as

I = ⅔MR² + MR²

I = 5/2 MR²

also, going forward, we assume d = R

next, we substitute each into the equation for period, i.e 2π√(I/mgd)

T = 2π √[(5/3MR²) / MgR]

T = 2π √[(5/3R) / g]

T = 2π √(5R/3g)

Next, we plug in the values of each, and we have

T = 2π √[(5 * 0.055) / (3 * 9.8)]

T = 2π √(0.275/29.4)

T = 2π √0.00935

T = 2π * 0.0967

T = 2 * 3.142 * 0.0967

T = 0.608 s

Therefore, the period of the hollow sphere is 0.608 s

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enot [183]

Answer:

A. U_0 = \dfrac{\epsilon_0 A V^2}{2d}

B. U_1 = \dfrac{\epsilon_0 A V^2}{6d}

C. U_2 = \dfrac{K\epsilon_0 A V^2}{2d}

Explanation:

The capacitance of a capacitor is its ability to store charges. For parallel-plate capacitors, this ability depends the material between the plates, the common plate area and the plate separation. The relationship is

C=\dfrac{\epsilon A}{d}

C is the capacitance, A is the common plate area, d is the plate separation and \epsilon is the permittivity of the material between the plates.

For air or free space, \epsilon is \epsilon_0 called the permittivity of free space. In general, \epsilon=\epsilon_r \epsilon_0 where \epsilon_r is the relative permittivity or dielectric constant of the material between the plates. It is a factor that determines the strength of the material compared to air. In fact, for air or vacuum, \epsilon_r=1.

The energy stored in a capacitor is the average of the product of its charge and voltage.

U = \dfrac{QV}{2}

Its charge, Q, is related to its capacitance by Q=CV (this is the electrical definition of capacitance, a ratio of the charge to its voltage; the previous formula is the geometric definition). Substituting this in the formula for U,

U = \dfrac{CV^2}{2}

A. Substituting for C in U,

U_0 = \dfrac{\epsilon_0 A V^2}{2d}

B. When the distance is 3d,

U_1 = \dfrac{\epsilon_0 A V^2}{2\times3d}

U_1 = \dfrac{\epsilon_0 A V^2}{6d}

C. When the distance is restored but with a dielectric material of dielectric constant, K, inserted, we have

U_2 = \dfrac{K\epsilon_0 A V^2}{2d}

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3 years ago
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7nadin3 [17]

Answer:

tympanic membrane (eardrum)

Explanation:

The sound waves spread through the air and reach the outer ear, into which they penetrate through the ear canal. In doing so, they stimulate the eardrum, which closes the inner end of the duct. By vibrating this membrane, the vibration of a chain of ossicles located in the middle ear is induced. These ossicles transmit their vibration to the oval window, which is a membranous structure that communicates the middle ear with the cochlea of ​​the inner ear. When the oval membrane moves, it moves the liquid (perilymph) that fills one of the three cavities of the cochlea generating waves in it. These waves mechanically stimulate the sensory cells (hair cells) located in the organ of Corti, within the cochlea in the central cavity, the middle ramp. This cavity is filled with a liquid rich in K +, endolymph. The cells embedded in the endolymph, change their permeability to K + due to the movement of the cilia and respond by releasing a neurotransmitter that excites the nerve terminals, which initiate the auditory sensory pathway.

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Answer:

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F=\frac {13.8 N.s}{0.001}=13800N

Therefore, the average force is equivalent to 13800 N

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