Ask question

Ask question

All categories

3 years ago

10

A horizontal 649 N merry-go-round of radius 1.05 m is started from rest by a constant horizontal force of 61.3 N applied tangent

ially to the merry-go-round. Find the kinetic energy of the merry-goround after 3.34 s. The acceleration of gravity is 9.8 m/s 2 . Assume the merry-go-round is a solid cylinder. Answer in units of J.

1 answer:

nexus9112 [7]3 years ago

4 0

Answer:

The kinetic energy of the merry-go-round is 632.82 J

Explanation:

Given;

weight of the merry-go-round, W = 649 N

radius of the merry-go-round, r = 1.05 m

applied horizontal force, F = 61.3 N

acceleration due to gravity, g = 9.8 m/s²

mass of merry-go-round, m = W/g

= 649/9.8 = 66.225 kg

moment of inertia of merry-go-round, I = ¹/₂mr²

= ¹/₂ x 66.225 x (1.05)²

= 36.507 kg.m²

Angular acceleration of the merry-go-round, α

τ = Iα = Fr

α = Fr / I

Where;

α is angular acceleration

α = (61.3 x 1.05) / 36.507

α = 1.763 rad/s²

Angular velocity of the merry-go-round, ω

ω = αt

ω = 1.763 x 3.34

ω = 5.888 rad/s

Finally, the kinetic energy of the merry-go-round, K.E

K.E = ¹/₂Iω²

K.E = ¹/₂ x 36.507 x (5.888)²

K.E = 632.82 J

You might be interested in

A slide whistle is an open-closed tube with an adjustable plunger that changes the length. You are playing the slide whistle and

Serjik [45]

Answer:

df / ft = -n 12 n= 1, 3, 5, ...

Explanation:

The speed of sound is

v = λ f

In a whistle that we approach by an open tube at one end and closed at the other, standing waves occur, which has a node in the closed part and a maximum in the open pate, whereby wavelength and the distance of the tube are related, the fundamental wave is

λ₁ = 4L

The harmonics are

λ₃ = 4L / 3

λ₅ = 4L / 5

The general formula

λₙ = 4L / n

with n = 1, 3, 5,…

We substitute and clear in the first equation

f = v n / 4L n = 1, 3, 5,…

Let's use derivatives to find the frequency change

df / dt = v n /4 dL⁻¹ / dt

d / dt (1/L) = - 1 / L² dL / dt

Where dL / dt = 8 cm / s

We replace

df / dt = - n v / L2 dL / dt

Let's calculate

df / dt = - n 340/152 8

df / ft = -n 12 n= 1, 3, 5, ...

4 0

4 years ago

Which equations could be used as is, or rearranged to calculate for frequency of a wave? Check all that apply.

amm1812

-- Equations #2 and #6 are both the same equation,
and are both correct.

-- If you divide each side by 'wavelength', you get Equation #4,
which is also correct.

-- If you divide each side by 'frequency', you get Equation #3,
which is also correct.
With some work, you can rearrange this one and use it to calculate
frequency.

Summary:

-- Equations #2, #3, #4, and #6 are all correct statements,
and can be used to find frequency.

-- Equations #1 and #5 are incorrect statements.

7 0

3 years ago

Read 2 more answers

Two guitarists attempt to play the same note of wavelength 6.50 cm at the same time, but one of the instruments is slightly out

PolarNik [594]

Answer:

The two value of the wavelength for the out of tune guitar is

$\lambda _2 = (6.48,6.52) \ cm$

Explanation:

From the question we are told that

The wavelength of the note is $\lambda = 6.50 \ cm = 0.065 \ m$

The difference in beat frequency is $\Delta f = 17.0 \ Hz$

Generally the frequency of the note played by the guitar that is in tune is

$f_1 = \frac{v_s}{\lambda}$

Where $v_s$ is the speed of sound with a constant value $v_s = 343 \ m/s$

$f_1 = \frac{343}{0.0065}$

$f_1 = 5276.9 \ Hz$

The difference in beat is mathematically represented as

$\Delta f = |f_1 - f_2|$

Where $f_2$ is the frequency of the sound from the out of tune guitar

$f_2 =f_1 \pm \Delta f$

substituting values

$f_2 =f_1 + \Delta f$

$f_2 = 5276.9 + 17.0$

$f_2 = 5293.9 \ Hz$

The wavelength for this frequency is

$\lambda_2 = \frac{343 }{5293.9}$

$\lambda_2 = 0.0648 \ m$

$\lambda_2 = 6.48 \ cm$

For the second value of the second frequency

$f_2 = f_1 - \Delta f$

$f_2 = 5276.9 -17$

$f_2 = 5259.9 Hz$

The wavelength for this frequency is

$\lambda _2 = \frac{343}{5259.9}$

$\lambda _2 = 0.0652 \ m$

$\lambda _2 = 6.52 \ cm$

8 0

3 years ago

Prove that the period of a simple pendulum T=2×22/7×rootl/g

Rudik [331]

Answer:

Explanation:

Check the attachment.

By the definition of the simple harmonic motion,

The motion of a particle whose acceleration is

1. Always directed towards the center of the motion.

2. Proportional to the distance from center of the motion.

We get, a ∝ -x

where

a = acceleration

x = distance of the particle from center of the motion

- sign says acceleration is in opposite direction of motion

Check the other attachment for proof of a = -ω²x (or a = -ω²y)

x and y are both use to denote distance from center of the motion

<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> pdf </span>

<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> pdf </span>

4 0

3 years ago

The chart shows the bids provided by four contractors to complete a job.

serg [7]

"Cost-effective" means "most economical", "lowest cost", "cheapest".

Joshua . . . charges $25 an hour, says the job will take him 5 hours. If Joshua is hired, then the total cost to get the job done is ($25/hr) x (5 hr) = <em>$125</em> .

Carmen . . . $20 per hour, 7 hours, total cost ($20/hr) x (7 hr) = $140

Dante . . . $30 per hour, 6 hours, total cost ($30/hr) x (6 hr) = $180

Alicia . . . $20 per hour, 8 hours, total cost ($20/hr) x (8 hr) = $160

<em>Joshua's</em> total bid cost is the lowest, so his company should get the job.

Notice that all of these bids are predictions of something that hasn't happened yet. <u><em>IF</em></u> Joshua can actually finish the job in 5 hours, like he says, then he would be the cheapest. But his estimate of the time required is the shortest of all. That's great if he's done this kind of job before. But if he doesn't have experience doing it, I would be a little careful. He could get part of the way through the job and discover that it's going to take him longer than he thought.

There are also certain regional considerations:

-- I live in Chicago, where cost is not always the main factor. Here, you would have to award the job to Dante, because his brother supplies the concrete in the ward where the job will be done, and his niece is dating the alderman of that ward.

-- In California, you'd have to give Alicia the job because the board of directors and management of her company are all women. You should also plan to provide chocolates, flowers, and college scholarships to her administrative staff and IT department relatively soon after the job is completed.

5 0

4 years ago