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Svet_ta [14]
3 years ago
15

Two children (m = 40 kg each) stand opposite each other on the edge of a merry-go-round. The merry-go-round, which has a mass M

of 200 kg and a radius of 2.0 m, is spinning at a constant rate of 12 rad/s. Treat the two children and the merry-go-round as a system. Both children walk half the distance toward the center of the merry-go-round. Calculate the final angular speed of the system.
Physics
1 answer:
s344n2d4d5 [400]3 years ago
3 0

Answer:

Explanation:

Initially the two boys were sitting on the periphery , total moment of inertia

= 1/2 M  r² + 2mr²     ; M is mass of the merry go round , m is mass of each boy and r is the radius

1/2 x 200 x 2² + 2 x 40 x 2²

= 400 + 320

I₁ =  720 kg m²

Finally  the two boys were sitting at the middle  , total moment of inertia

= 1/2 M  r² + 2m( r/2)²     ; M is mass of the merry go round , m is mass of each boy and r is the radius

1/2 x 200 x 2² + 2 x 40 x 1²

= 400 + 80

I₂  = 480

Now the system will obey law of coservation of angular momentum because no torque is acting on the system.

I₁ω₁ =  I₂ω₂ ,         I₁  and ω₁  are moment of inertia and angular velocity of first case and  I₂  and ω₂ are of second case.

720 X 12 = 480 ω₂

ω₂ = 18 rad / s

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How do your results from ray tracing compare to your results from using the thin-lens equation?
EastWind [94]

Answer:

20cm

Explanation:

A convex lens has a positive focal length and the object placed in front of it produce both virtual and real image <em>(image distance can be negative or positive depending on the nature of the image</em>).

According to the lens equation

\frac{1}{f} = \frac{1}{u} + \frac{1}{v} where;

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u is the object distance

v is the image distance

If the magnification is - 0.6

mag = v/u = -0.5

v = -0.5u

since v = 10cm

10 = -0.5u

u = -10/0.5

u =-20 cm

Substitute u = -20cm ( due to negative magnification)and v = 10cm into the lens formula to get the focal length f

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\\\frac{1}{f} = \frac{1}{-20} + \frac{1}{10}\\\frac{1}{f} = \frac{1}{-20} + \frac{1}{10}\\\frac{1}{f} = \frac{-1+2}{20} \\\frac{1}{f} = \frac{1}{20} \\cross \ multiply\\f = 20\\f = 20 cm

Hence the focal length of the convex lens is 20cm

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Sound waves that enter the external acoustic meatus eventually encounter the __________, which then vibrates at the same frequen
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.

3 0
3 years ago
A flute player hears four beats per second when she compares her note to a 523 HzHz tuning fork (the note C). She can match the
laiz [17]

Answer:

527 Hz

Solution:

As per the question:

Beat frequency of the player, \Delta f = 4\ beats/s

Frequency of the tuning fork, f = 523 Hz

Now,

The initial frequency can be calculated as:

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f_{i} = f \pm \Delta f

when

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when

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But we know that as the length of the flute increases the frequency decreases

Hence, the initial frequency must be 527 Hz

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3 years ago
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